Results 11 to 20 of about 136,759 (108)
Sectional curvatures of K�hler moduli
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]
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]
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
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]
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]
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
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]
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
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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