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Kwang-soon Park - One of the best experts on this subject based on the ideXlab platform.
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On the Pointwise Slant Submanifolds
Hermitian–Grassmannian Submanifolds, 2017Co-Authors: Kwang-soon ParkAbstract:In this survey paper, we consider several kinds of submanifolds in Riemannian manifolds, which are obtained by many authors. (i.e., slant submanifolds, Pointwise slant submanifolds, semi-slant submanifolds, Pointwise semi-slant submanifolds, Pointwise almost h-slant submanifolds, Pointwise almost h-semi-slant submanifolds, etc.) And we deal with some results, which are obtained by many authors at this area. Finally, we give some open problems at this area.
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Pointwise almost h-semi-slant submanifolds
International Journal of Mathematics, 2015Co-Authors: Kwang-soon ParkAbstract:We introduce the notions of Pointwise almost h-slant submanifolds and Pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, Pointwise slant submanifolds, semi-slant submanifolds, and Pointwise semi-slant submanifolds. We obtain a characterization and investigate the following: the integrability of distributions, the conditions for such distributions to be totally geodesic foliations, the properties of h-slant functions and h-semi-slant functions, the properties of nontrivial warped product proper Pointwise h-semi-slant submanifolds. We also obtain the topological properties of proper Pointwise almost h-slant submanifolds and give an inequality for the squared norm of the second fundamental form in terms of a warping function and a h-semi-slant function for a warped product submanifold of a hyperkahler manifold. Finally, we give some examples of such submanifolds.
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Pointwise slant and Pointwise semi-slant submanifolds in almost contact metric manifolds
arXiv: Differential Geometry, 2014Co-Authors: Kwang-soon ParkAbstract:As a generalization of slant submanifolds and semi-slant submanifolds, we introduce the notions of Pointwise slant submanifolds and Pointwise semi-slant sunmanifolds of an almost contact metric manifold. We obtain a characterization at each notion, investigate the topological properties of Pointwise slant submanifolds, and give some examples of them. We also consider some distributions on cosymplectic, Sasakian, Kenmotsu manifolds and deal with some properties of warped product Pointwise semi-slant submanifolds. Finally, we give some inequalities for the squared norm of the second fundamental form in terms of a warping function and a semi-slant function for warped product submanifolds of cosymplectic, Sasakian, Kenmotsu manifolds.
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Pointwise almost h-semi-slant submanifolds
arXiv: Differential Geometry, 2013Co-Authors: Kwang-soon ParkAbstract:We introduce the notions of Pointwise almost h-slant submanifolds and Pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, Pointwise slant submanifolds, semi-slant submanifolds, and Pointwise semi-slant submanifolds. We have characterizations and investigate the integrability of distributions, the conditions for such distributions to be totally geodesic foliations, the mean curvature vector fields on totally umbilic submanifolds, the properties of h-slant functions and h-semi-slant functions, the properties of non-trivial warped product proper Pointwise h-semi-slant submanifolds. We also obtain topological properties on proper Pointwise almost h-slant submanifolds and give an inequality for the squared norm of the second fundamental form in terms of the warping function and h-semi-slant functions for a warped product submanifold in a hyperk\"ahler manifold. Finally, we give some examples of such submanifolds.
Antti V Vahakangas - One of the best experts on this subject based on the ideXlab platform.
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self improvement of weighted Pointwise inequalities on open sets
Journal of Functional Analysis, 2020Co-Authors: Sylvester Erikssonbique, Juha Lehrback, Antti V VahakangasAbstract:Abstract We prove a general self-improvement property for a family of weighted Pointwise inequalities on open sets, including Pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of p-Poincare and p-Hardy weights for an open set Ω ⊂ X , where X is a metric measure space. We also apply the self-improvement of weighted Pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.
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self improvement of weighted Pointwise inequalities on open sets
arXiv: Classical Analysis and ODEs, 2020Co-Authors: Sylvester Erikssonbique, Juha Lehrback, Antti V VahakangasAbstract:We prove a general self-improvement property for a family of weighted Pointwise inequalities on open sets, including Pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincare and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted Pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.
Fu-gui Shi - One of the best experts on this subject based on the ideXlab platform.
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Pointwise PSEUDO-METRIC ON THE L-REAL LINE
Iranian Journal of Fuzzy Systems, 2005Co-Authors: Fu-gui ShiAbstract:In this paper, a Pointwise pseudo-metric function on the L-real line is constructed. It is proved that the topology induced by this Pointwise pseudo-metric is the usual topology.
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The category of Pointwise S-proximity spaces
Fuzzy Sets and Systems, 2005Co-Authors: Fu-gui ShiAbstract:First it is proved that the category of Pointwise quasi-uniform spaces and Pointwise quasi-uniformly continuous morphisms is topological. Then the concept of Pointwise S-quasi-proximity on lattice-valued fuzzy set theory is introduced in such a way as to be compatible with Pointwise quasi-uniformity and Pointwise p.q. metric. Each co-topology can be induced by a Pointwise S-quasi-proximity. When a valued lattice is a completely distributive lattices equipped with an order-reversing involution, the concept of Pointwise S-proximity can be defined by means of Pointwise S-quasi-proximity. The relation between Pointwise S-(quasi-)proximities and Pointwise (quasi-)uniformities is discussed. It is proved that the category of Pointwise S-quasi-proximity spaces is isomorphic to the category of totally bounded Pointwise quasi-uniform spaces. The category of Pointwise S-proximity spaces is isomorphic to a subcategory of totally bounded Pointwise uniform spaces. Hence they are topological.
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Pointwise pseudo-metrics in L -fuzzy set theory
Fuzzy Sets and Systems, 2001Co-Authors: Fu-gui ShiAbstract:A theory of Pointwise (pseudo-)metrics is based on L-fuzzy sets. A Pointwise pseudo-metric is characterized by its remote-neighborhood maps. Many theorems in general topology are generalized on L-fuzzy sets. The L-fuzzy real line and the L-fuzzy unit interval are Pointwise pseudo-metrizable. A pseudo-metrization theorem of Pointwise uniformity is obtained. Relations between Erceg's p. metric (pseudometric) and Pointwise p. metric are discussed.
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Pointwise uniformities and Pointwise metrics on fuzzy lattices
Chinese Science Bulletin, 1997Co-Authors: Fu-gui ShiAbstract:UP till now there has been much spectacular and creative work about the theories of uniformi-ties and metrics in topological lattice.But this is mostly generalizations and developmentsof Hutton’s and Erceg’s pointless work.They cannot directly reflect the characteristics ofPointwise topology.In this note we shall set up a theory of Pointwise uniformity and a theoryof Pointwise metric on fuzzy lattices.
A Sharma - One of the best experts on this subject based on the ideXlab platform.
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Pointwise pseudo slant warped product submanifolds in a kahler manifold
Mediterranean Journal of Mathematics, 2017Co-Authors: S K Srivastava, A SharmaAbstract:The purpose of this paper is to study the Pointwise pseudo-slant warped product submanifolds of a Kahler manifold \(\widetilde{M}\). We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a Pointwise pseudo-slant submanifolds of \(\widetilde{M}\). The necessary and sufficient conditions for isometrically immersed Pointwise pseudo-slant submanifolds of \(\widetilde{M}\) to be a Pointwise pseudo-slant warped product and a locally Riemannian product are obtained. Further, we classify Pointwise pseudo-slant warped product submanifolds of \(\widetilde{M}\) by developing the sharp inequalities in terms of second fundamental form and wrapping function.
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geometry of Pointwise pseudo slant warped product submanifolds in a k ahler manifold
arXiv: Differential Geometry, 2015Co-Authors: S K Srivastava, A SharmaAbstract:The purpose of this paper is to study Pointwise pseudo-slant warped product submanifolds of a Kahler manifold $\widetilde{M}$. We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a Pointwise pseudo-slant submanifold of $\widetilde{M}$. The necessary and sufficient conditions for isometrically immersed Pointwise pseudo-slant submanfold of $\widetilde{M}$ to be a Pointwise pseudo-slant warped product and a locally Riemannian product are obtained.
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Pointwise pseudo-slant submanifold of a para-Kaehler manifold
2015Co-Authors: S K Srivastava, A SharmaAbstract:The purpose of this paper is to study Pointwise pseudo-slant warped product submanifolds of a Kahler manifold $\widetilde{M}$. We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a Pointwise pseudo-slant submanifold of $\widetilde{M}$. The necessary and sufficient conditions for isometrically immersed Pointwise pseudo-slant submanfold of $\widetilde{M}$ to be a Pointwise pseudo-slant warped product and a locally Riemannian product are obtained.
Sylvester Erikssonbique - One of the best experts on this subject based on the ideXlab platform.
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self improvement of weighted Pointwise inequalities on open sets
Journal of Functional Analysis, 2020Co-Authors: Sylvester Erikssonbique, Juha Lehrback, Antti V VahakangasAbstract:Abstract We prove a general self-improvement property for a family of weighted Pointwise inequalities on open sets, including Pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of p-Poincare and p-Hardy weights for an open set Ω ⊂ X , where X is a metric measure space. We also apply the self-improvement of weighted Pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.
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self improvement of weighted Pointwise inequalities on open sets
arXiv: Classical Analysis and ODEs, 2020Co-Authors: Sylvester Erikssonbique, Juha Lehrback, Antti V VahakangasAbstract:We prove a general self-improvement property for a family of weighted Pointwise inequalities on open sets, including Pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincare and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted Pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.
