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N A Tyurin - One of the best experts on this subject based on the ideXlab platform.
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universal maslov class of a bohr sommerfeld lagrangian embedding into a pseudo Einstein Manifold
Theoretical and Mathematical Physics, 2007Co-Authors: N A TyurinAbstract:We show that in the case of a Bohr-Sommerfeld Lagrangian embedding into a pseudo-Einstein symplectic Manifold, a certain universal 1-cohomology class, analogous to the Maslov class, can be defined. In contrast to the Maslov index, the presented class is directly related to the minimality problem for Lagrangian subManifolds if the ambient pseudo-Einstein Manifold admits a Kahler-Einstein metric. We interpret the presented class geometrically as a certain obstruction to the continuation of one-dimensional supercycles from the Lagrangian subManifold to the ambient symplectic Manifold.
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universal maslov class of bohr sommerfeld lagrangian embedding to pseudo Einstein Manifold
arXiv: Symplectic Geometry, 2006Co-Authors: N A TyurinAbstract:In this paper we define the universal Maslov class of a Bohr - Sommerfeld lagrangian embedding to a simply connected pseudo - Einstein symplectic Manifold. This class is an invariant of hamiltonian (isodrastic) deformations of a given Bohr - Sommerfeld lagrangian subManifold.
Arindam Bhattacharyya - One of the best experts on this subject based on the ideXlab platform.
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On some classes of mixed-super quasi-Einstein Manifolds
Acta Universitatis Sapientiae Mathematica, 2016Co-Authors: Santu Dey, Buddhadev Pal, Arindam BhattacharyyaAbstract:Abstract Quasi-Einstein Manifold and generalized quasi-Einstein Manifold are the generalizations of Einstein Manifold. The purpose of this paper is to study the mixed super quasi-Einstein Manifold which is also the generalizations of Einstein Manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this Manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.
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a characterization of warped product on mixed super quasi Einstein Manifold
Journal of Dynamical Systems and Geometric Theories, 2014Co-Authors: Buddhadev Pal, Arindam BhattacharyyaAbstract:AbstractIn this paper we investigate the expressions of the Ricci tensors and scalar curvatures of warped product Manifold with respect to the bases and fibres when warped product Manifold is a mixed super quasi-Einstein Manifold. In some cases we give some obstructions to the existence of such Manifolds and in the last section we give an example of warped product on mixed super quasi-Einstein Manifold.
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CHARACTERIZATION OF SUPER QUASI-Einstein Manifold
Annals of the Alexandru Ioan Cuza University - Mathematics, 2014Co-Authors: K. Halder, Buddhadev Pal, Arindam BhattacharyyaAbstract:In this paper we give characterizations of super quasi-Einstein Manifold, mixed super quasi-Einstein Manifold and mixed generalized quasi-Einstein Manifold for both even and odd dimensions. Mathematics Subject Classication 2010: 53C25.
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Ricci Flow as a Gradient Flow on Some Quasi Einstein Manifolds
2012Co-Authors: Srabani Panda, Arindam BhattacharyyaAbstract:In this paper we study gradient Ricci flow on n dimensional quasi Einstein Manifold with an example on 5-dimension. We have also studied quasi conformally flat quasi Einstein Manifold and gradient Ricci flow on four dimensional quasi conformally flat quasi Einstein Manifold.
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ricci flow on quasi Einstein Manifold
Annals of the Alexandru Ioan Cuza University - Mathematics, 2010Co-Authors: Arindam BhattacharyyaAbstract:In this paper we study the Ricci flow on a quasi Einstein Manifold, obtained some results on basic control of the scalar curvature and volume of the Manifold. Mathematics Subject Classication 2000: 53C44, 53C21, 58J35.
Kouei Sekigawa - One of the best experts on this subject based on the ideXlab platform.
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A generalization of a 4-dimensional Einstein Manifold
Mathematica Slovaca, 2013Co-Authors: Yunhee Euh, Jeonghyeong Park, Kouei SekigawaAbstract:A weakly Einstein Manifold is a natural generalization of a 4-dimensional Einstein Manifold. In this paper, we shall give a characterization of a weakly Einstein Manifold in terms of so-called generalized Singer-Thorpe bases. As an application, we prove a generalization of the Hitchin inequality for compact weakly Einstein 4-Manifolds. Examples are provided to illustrate the theorems.
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A generalization of a 4-dimensional Einstein Manifold
arXiv: Differential Geometry, 2010Co-Authors: Yunhee Euh, Jeonghyeong Park, Kouei SekigawaAbstract:A weakly Einstein Manifold is a generalization of a 4-dimensional Einstein Manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian Manifold. In this paper, we shall give a characterization of a weakly Einstein Manifold.
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Remarks on η-Einstein unit tangent bundles
Monatshefte für Mathematik, 2008Co-Authors: Y. D. Chai, S. H. Chun, Jeonghyeong Park, Kouei SekigawaAbstract:We study the geometric properties of the base Manifold for the unit tangent bundle satisfying the η-Einstein condition with the canonical contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein Manifold, equipped with the canonical contact metric structure, is η-Einstein Manifold if and only if the base Manifold is the space of constant sectional curvature 1 or 2.
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Remarks on $\eta$-Einstein unit tangent bundles
arXiv: Differential Geometry, 2007Co-Authors: Y. D. Chai, S. H. Chun, J. H. Park, Kouei SekigawaAbstract:We study the geometric properties of the base Manifold for the unit tangent bundle satisfying the $\eta$-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein Manifold, equipped with the canonical contact metric structure, is $\eta$-Einstein Manifold if and only if base Manifold is the space of constant sectional curvature 1 or 2.
Romildo Pina - One of the best experts on this subject based on the ideXlab platform.
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Quasi-Einstein Manifolds with structure of warped product
Differential Geometry and its Applications, 2020Co-Authors: Paula Correia, Romildo PinaAbstract:Abstract In this paper we prove that, under certain conditions, in a quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein Manifold. We provide all the quasi-Einstein Manifolds when r-Bakry-Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an ( n − 1 ) -dimensional translation group and the fiber is Ricci-flat. As an application, we have built a family of Ricci-flat Einstein warped product whose base is not locally conformally flat.
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An analysis of symmetry groups of generalized $m$-quasi-Einstein Manifolds
arXiv: Differential Geometry, 2019Co-Authors: Paula Correia, Benedito Leandro, Romildo PinaAbstract:In this paper emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the generalized $m$-quasi-Einstein Manifold, and vice versa. Considering a $n$-dimensional generalized $m$-quasi-Einstein Manifold which is conformal to a pseudo-Euclidean space, we prove the most general symmetry group of maximal dimension. Moreover, we demonstrate that there is no different low dimensional invariant on a generalized $m$-quasi-Einstein Manifold. As an application, we use the invariant structure of the metric to provide an example of shrinking $m$-quasi-Einstein Manifold (cf. Example 3). A discussion about the fluid ball conjecture was made.
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Quasi-Einstein Manifolds with structure of warped product product
arXiv: Differential Geometry, 2019Co-Authors: Paula Gonçalves Correia Bonfim, Romildo PinaAbstract:In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein Manifold. We provide all the quasi Einstein Manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action of an n - 1 dimensional translation group and the fiber is Ricci flat. As an application, we have built a family of Ricci flat Einstein warped product whose base is not locally conformally flat.
Yuji Tachikawa - One of the best experts on this subject based on the ideXlab platform.
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Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies
arXiv: High Energy Physics - Theory, 2012Co-Authors: Richard Eager, Johannes Schmude, Yuji TachikawaAbstract:The superconformal index of the quiver gauge theory dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein Manifold with five-dimensional AdS space is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Along the way, we find that the index on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of the Sasaki-Einstein Manifold and that the index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver.
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Triangle Anomalies from Einstein Manifolds
arXiv: High Energy Physics - Theory, 2006Co-Authors: Sergio Benvenuti, Leopoldo A. Pando Zayas, Yuji TachikawaAbstract:The triangle anomalies in conformal field theory, which can be used to determine the central charge a, correspond to the Chern-Simons couplings of gauge fields in AdS under the gauge/gravity correspondence. We present a simple geometrical formula for the Chern-Simons couplings in the case of type IIB supergravity compactified on a five-dimensional Einstein Manifold X. When X is a circle bundle over del Pezzo surfaces or a toric Sasaki-Einstein Manifold, we show that the gravity result is in perfect agreement with the corresponding quiver gauge theory. Our analysis reveals an interesting connection with the condensation of giant gravitons or dibaryon operators which effectively induces a rolling among Sasaki-Einstein vacua.
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Triangle anomalies from Einstein Manifolds
Advances in Theoretical and Mathematical Physics, 2006Co-Authors: Sergio Benvenuti, Leopoldo A. Pando Zayas, Yuji TachikawaAbstract:The triangle anomalies in conformal field theory, which can be used to determine the central charge a, correspond to the Chern-Simons couplings of gauge fields in AdS5 under the gauge/gravity correspondence. We present a simple geometrical formula for the Chern-Simons couplings in the case of type IIB supergravity compactified on a five-dimensional Einstein Manifold X. When X is a toric Sasaki-Einstein Manifold, we show that the gravity result is in perfect agreement with the corresponding quiver gauge theory. This article is based on the work [1] by the speaker, S. Benvenuti and L. A. Pando Zayas.