Results 21 to 30 of about 1,746,741 (337)
Pointwise orthogonal splitting of the space of TT-tensors
Дифференциальная геометрия многообразий фигур, 2023 In the present paper we consider pointwise orthogonal splitting of the space of well-known TT-tensors on Riemannian manifolds. Tensors of the first subspace belong to the kernel of the Bourguignon Laplacian, and the tensors of the second subspace ...
S. E. Stepanov, I. I. Tsyganok
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Sweeping out sectional curvature [PDF]
Geometry & Topology, 2014 We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.
Panov, D., Petrunin, A.
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On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection
Дифференциальная геометрия многообразий фигур, 2023 In this article, a sub-Riemannian manifold of contact type is understood as a Riemannian manifold equipped with a regular distribution of codimension-one and by a unit structure vector field orthogonal to this distribution. This vector field is called a
S. V. Galaev
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Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics [PDF]
Science China Mathematics, 2019 We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal Kähler manifold with constant nonpositive holomorphic sectional curvature is Kähler. We also give
Haojie Chen, Lin Chen, Xiaolan Nie
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Highly connected 7-manifolds and non-negative sectional curvature
Annals of Mathematics, 2020 Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that
S. Goette, M. Kerin, K. Shankar
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On projective manifolds with semi-positive holomorphic sectional curvature [PDF]
American Journal of Mathematics, 2018 :We establish structure theorems for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. We first prove that $X$ is rationally connected if $X$ has no truly flat tangent vectors at some point (which is satisfied when the ...
Shin-ichi Matsumura
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On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature [PDF]
Pure and Applied Mathematics Quarterly, 2018 In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature.
Shin-ichi Matsumura
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K- constant type Kahler and Nearly Kahler manifolds for conharmonic curvature tensor
Tikrit Journal of Pure Science, 2023 The constant of permanence conharmonic type kahler and nearly kahler manifold conditions are obtained when the Nearly Kahler manifold is a manifold conharmonic constant type (K).
Ali A. Shihab, Rana H. jasim
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Quasiprojective manifolds with negative holomorphic sectional curvature [PDF]
Duke mathematical journal, 2018 Let $(M,\omega)$ be a compact K\"ahler manifold with negative holomorphic sectional curvature. It was proved by Wu-Yau and Tosatti-Yang that $M$ is necessarily projective and has ample canonical bundle.
Henri Guenancia
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Geometric inequalities for hypersurfaces with nonnegative sectional curvature in hyperbolic space [PDF]
Calculus of Variations and Partial Differential Equations, 2018 In this article, we will use inverse mean curvature flow to establish an optimal Sobolev-type inequality for hypersurfaces $$\Sigma $$Σ with nonnegative sectional curvature in $$\mathbb {H}^n$$Hn.
Yingxiang Hu, Haizhong Li
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