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Curvature is a notion originally developed in differential and Riemannian geometry. It was then discovered that curvature inequalities in Riemannian manifolds are equivalent to other geometric propert...
Let p : X ! S be a smooth K¨ahler fibration and E ! X a Hermitian holomorphic vector bundle. As motivated by the work of Berdtsson([Bern09]), by using basic Hodge theory, we derive several general cur...
Abstract: We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvature metrics ...
The Lie group SO0(n, 1) has the left-invariant metric com-ing from the Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group acts from the left. The geometry of the quo-tient s...
For a large class of self-similar random sets F in Rd geometric parameters Ck(F), k = 0, . . . , d, are introduced. They arise as a.s. (average or essential) limits of the volume Cd(F(")), the surface...
<正> Su has recently established the projective theory of space curvesby a purely geometrical method and has shown among other thingsthat the projective invariants of a curve can simply be expressed by...
Let M be a compact Riemannian manifold of dimension n. The k-curvature,for k = 1; 2; ¢ ¢ ¢ ; n, is defined as the k-th elementary symmetric polynomial of the eigenvalues of the Schouten tenser. The k-...

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