Results 11 to 20 of about 136,759 (108)
Sectional curvatures of K�hler moduli
Mathematische Annalen, 2004 We investigate a new property for compact Kahler manifolds. Let X be a Kahler manifold of dimension n and let H^{1,1} denote the (1,1) part of its real second cohomology. On this space, we have an degree n form given by cup product. Let K denote the open cone of Kahler classes in H^{1,1}, and K_1 the level set consisting of classes in K on which the n ...
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Group-Quotients with Positive Sectional Curvatures [PDF]
Proceedings of the American Mathematical Society, 1977 Let H be a closed subgroup of compact Lie group G. A necessary and sufficient condition is obtained for the existence of a left-invariant Riemannian metric on G such that the subduced metric on the quotient H G has strictly positive sectional curvatures.
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Curvature and Concentration of Hamiltonian Monte Carlo in High Dimensions [PDF]
, 2015 In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold.
Holmes, Susan +2 more
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Smoothing metrics on closed Riemannian manifolds through the Ricci flow
, 2011 Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound.
Yang, Yunyan
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Holomorphic sectional curvature of quasisymmetric domains [PDF]
Proceedings of the American Mathematical Society, 1979 It is well known that the holomorphic sectional curvature of a bounded symmetric domain is bounded above by a negative constant. In this paper we show that this is true more generally for a quasi-symmetric Siegel domain, and the proof is based on a formula for the curvature from the author’s thesis. The bounded homogeneous domains are, as is well known,
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Complete hypersurfaces with constant mean curvature and nonnegative sectional curvatures [PDF]
Proceedings of the American Mathematical Society, 1995 We classify the complete and non-negatively curved hypersurfaces of constant mean curvature in spaces of constant sectional curvature.
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Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature
Acta Mathematica Sinica, English Series, 2022 A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler when the constant is non-zero and must be Chern flat when the constant is zero. The conjecture is known in complex dimension $2$ by the work of Balas-Gauduchon in 1985 (when the constant is zero or negative)
Rao, Pei Pei, Zheng, Fang Yang
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The Geometry of Axisymmetric Ideal Fluid Flows with Swirl [PDF]
, 2014 The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold $M$ can give information about the stability of inviscid, incompressible fluid flows on $M$.
Preston, Stephen C., Washabaugh, Pearce
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Positivity and Kodaira embedding theorem
, 2020 Kodaira embedding theorem provides an effective characterization of projectivity of a K\"ahler manifold in terms the second cohomology. Recently X. Yang [21] proved that any compact K\"ahler manifold with positive holomorphic sectional curvature must be ...
Ni, Lei, Zheng, Fangyang
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