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Scalar curvature
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We consider statistical submanifolds in Sasaki-like statistical manifolds. We give some examples of invariant and antiinvariant submanifolds of Sasaki-like statistical manifolds. We prove Chen-like inequality involving scalar curvature and Chen–Ricci inequality for these kinds of submanifolds.
15p
nutifooddau
21-01-2019
13
2
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In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the k-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-slant submanifold in a cosymplectic space form of constant ϕ- sectional curvature with arbitrary codimension.
14p
danhdanh27
07-01-2019
11
1
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In this paper, we study slant submanifolds of a Kaehler product manifold. We show that an F-invariant slant submanifold of Kaehler product manifold is a product manifold. We also obtain some curvature inequalities in terms of scalar curvature and Ricci tensor.
13p
danhdanh27
07-01-2019
21
1
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In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasiconstant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.
9p
tuongvidanh
06-01-2019
22
2
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In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case. We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric.
10p
tuongvidanh
06-01-2019
18
1
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In this paper, the induced Ricci tensor and the extrinsic scalar curvature on lightlike submanifolds are obtained. This scalar quantity extend the result given by C. Atindogbe in. An example of extrinsic scalar curvature on one class of 2-degenerate manifolds is provided.
19p
tuongvidanh
06-01-2019
14
1
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This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordstr¨m data, o the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose. ...
55p
tuanloccuoi
04-01-2013
54
6
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Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields 5. Tensor Fields 6. Riemannian Manifolds 7. Locally Minkowskian Manifolds: An Introduction to Relativity 8.
128p
khangoc2391
11-08-2012
53
1
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