The Experts below are selected from a list of 261 Experts worldwide ranked by ideXlab platform
Fangyang Zheng - One of the best experts on this subject based on the ideXlab platform.
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Complex nilmanifolds and K\"ahler-like Connections
arXiv: Differential Geometry, 2019Co-Authors: Quanting Zhao, Fangyang ZhengAbstract:In this note, we analyze the question of when will a complex nilmanifold have Kahler-like Strominger (also known as Bismut), Chern, or Riemannian Connection, in the sense that the curvature of the Connection obeys all the symmetries of that of a Kahler metric. We give a classification in the first two cases and a partial description in the third case. It would be interesting to understand these questions for all Lie-Hermitian manifolds, namely, Lie groups equipped with a left invariant complex structure and a compatible left invariant metric.
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Complex nilmanifolds and Kähler-like Connections
Journal of Geometry and Physics, 2019Co-Authors: Quanting Zhao, Fangyang ZhengAbstract:Abstract In this note, we analyze the question of when will a complex nilmanifold have Kahler-like Strominger (also known as Bismut), Chern, or Riemannian Connection, in the sense that the curvature of the Connection obeys all the symmetries of that of a Kahler metric. We give a classification in the second case and a partial description in the first and the third case. It would be interesting to understand these questions for all Lie–Hermitian manifolds, namely, Lie groups equipped with a left invariant complex structure and a compatible left invariant metric.
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The set of all orthogonal complex structures on the flat 6-tori
Advances in Mathematics, 2017Co-Authors: Gabriel Khan, Bo Yang, Fangyang ZhengAbstract:Abstract In [2] , Borisov, Salamon and Viaclovsky constructed non-standard orthogonal complex structures on flat tori T R 2 n for any n ≥ 3 . We will call these examples BSV-tori. In this note, we show that on a flat 6-torus, all the orthogonal complex structures are either the complex tori or the BSV-tori. This solves the classification problem for compact Hermitian manifolds with flat Riemannian Connection in the case of complex dimension three.
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The set of all orthogonal complex structures on the flat $6$-tori
arXiv: Differential Geometry, 2016Co-Authors: Gabriel Khan, Bo Yang, Fangyang ZhengAbstract:In \cite{BSV}, Borisov, Salamon and Viaclovsky constructed non-standard orthogonal complex structures on flat tori $T^{2n}_{\mathbb R}$ for any $n\geq 3$. We will call these examples BSV-tori. In this note, we show that on a flat $6$-torus, all the orthogonal complex structures are either the complex tori or the BSV-tori. This solves the classification problem for compact Hermitian manifolds with flat Riemannian Connection in the case of complex dimension three.
C. S. Bagewadi - One of the best experts on this subject based on the ideXlab platform.
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On Quarter-Symmetric Metric Connection in a Lorentzian Para-Sasakian Manifold (pp.3-12)
Azerbaijan Journal of Mathematics, 2014Co-Authors: V. Venkatesha, K. T. Pradeep Kumar, C. S. BagewadiAbstract:In this paper we obtain results on symmetric and concircular symmetric Lorentzianpara-Sasakian (briefly LP-Sasakian) manifolds with respect to quarter-symmetric metric connec-tion and Riemannian Connection.
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On -Recurrent Para-Sasakian Manifold AdmittingQuarter-Symmetric Metric Connection
ISRN Geometry, 2012Co-Authors: K. T. Pradeep Kumar, Venkatesha, C. S. BagewadiAbstract:We obtained the relation between the Riemannian Connection and the quarter-symmetric metric Connection on a para-Sasakian manifold. Further, we study
Gamal G. L. Nashed - One of the best experts on this subject based on the ideXlab platform.
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Regularization of Kerr-NUT spacetimes and their thermodynamical quantities
Progress of Theoretical Physics, 2012Co-Authors: Gamal G. L. NashedAbstract:In the context of the teleparallel equivalent of general relativity (TEGR) theory, continues calculations of the total energy and momentum for Kerr-NUT spacetimes using three different methods, the gravitational energy-momentum, the Riemannian Connection 1-form, ${\widetilde{\Gamma}_\alpha}^\beta$ and the Euclidean continuation method, have been achieved. Many local Lorentz transformations, that play the role of regularizing tool, are given to get the commonly known form of energy and momentum. We calculate the thermodynamic quantities of Kerr-NUT spacetime. We also investigate the first law of thermodynamics and quantum statistical relation.
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On the Regularization of Kerr-NUT spacetime: I
Progress of Theoretical Physics, 2012Co-Authors: Gamal G. L. NashedAbstract:Within the framework of teleparallel equivalent of general relativity (TEGR) theory, calculation of the total energy and momentum of Kerr-NUT spacetimes have been employed using two methods of the gravitational energy-momentum, which is coordinate independent, and the Riemannian Connection 1-form, ${\widetilde{\Gamma}_\alpha}^\beta$. It has been shown that the two methods give the same an unacceptable result, i.e., divergent value. Therefore, a local Lorentz transformation that plays a role of a regularizing tool, which subtracts the inertial effects without distorting the true gravitational contribution, has been suggested. This transformation keeps the resulting spacetime to be a solution of the equations of motion of TEGR.
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Kerr-Taub-NUT General Frame, Energy, and Momentum in Teleparallel Equivalent of General Relativity
Advances in High Energy Physics, 2012Co-Authors: Gamal G. L. NashedAbstract:A new exact solution describing a general stationary and axisymmetric object of the gravitational field in the framework of teleparallel equivalent of general relativity (TEGR) is derived. The solution is characterized by three parameters “the gravitational mass
Jagannath Chowdhury - One of the best experts on this subject based on the ideXlab platform.
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A Note On The Quasi-Conformal And M-Projective Curvature Tensor Of A Semi-Symmetric Recurrent Metric Connection On A Riemannian Manifold
2019Co-Authors: Rajesh Kumar, Jagannath ChowdhuryAbstract:Abstract: In the present note we have considered Mn to be a Riemannian manifold admitting a semi-symmetric recurrent metric Connection. The aim of the present paper is to obtain the conditions under which the quasi-conformal curvature tensor and M-projective curvature tensor of semi-symmetric recurrent metric Connection and the Riemannian Connection to be equal.Key words: Semi-symmetric recurrent metric Connection, quasi-conformal curvature tensor, M-projective curvature tensor.
R. P. Kushwaha - One of the best experts on this subject based on the ideXlab platform.
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Lorentzian Para Sasakian Manifolds Admitting Special Semi Symmetric Recurrent Metric Connection
Global Journal of Science Frontier Research, 2013Co-Authors: Sunil Kumar Srivastava, R. P. KushwahaAbstract:Several author as Agashe and Chafle [1], Sengupta, De. U.C, Binh [4] and many other introduced semi symmetric non metric Connection in different way. In this paper we have studied LP sasakian manifold with special semi-symmetric recurrent metric Connection [2] and discuss it exientance in LP sasakian manifold. In section 3 we establish the relation between the Riemannian Connection and special semi-symmetric recurrent metric Connection on LP sasakian manifold [4]. The section 4 deals with ξ–conformaly flat and ∅ concircularly flat of n dimensional LP sasakian manifold and we proved that ξ–conformaly flatness with special semi-symmetric recurrent metric Connection and Riemannian manifold coincide.
