We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson [8, 9], which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant scalar curvature metrics in Sasaki geometry with only few modification. We prove that the space of Sasaki metrics is an infinite dimens...

Although the autoparallel curves and geodesics coincide in Riemannian geometry which only curvature is nonzero among nonmetricity, torsion curvature, they define different non-Riemannian ones. We give a novel approach to for theories of symmetric teleparallel gravity written coincident gauge. Then we apply our equation Schwarzschild-type metric remarks about dark matter orbit equation.

We study maximally symmetric cosmological solutions of type II supersym-metric strings in the presence of the exact quartic curvature corrections to the lowest order effective action, including loop and D-instanton effects. We find that, unlike the case of type IIA theories, de Sitter solutions exist for type IIB superstrings, a conclusion that remains valid when higher-curvature corrections ar...

Second derivative pinching estimates are proved for a class of elliptic and parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B. Chow and the author. The result is obtained via a detailed ...

Introduction. In [5], J. Milnor cited "understanding the Ricci tensor Rik = J^ Rt'kl 9J as a fundamental problem of present-day mathematics. A basic issue, then, is to determine which symmetric covariant tensors of rank two can be Ricci tensors of Riemannian metrics. The definition of Ricci curvature casts the problem of finding a metric g which realizes a given Ricci curvature R as one of solv...

We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space HH. This deformation includes a c...

2014 Shapes of closed fluid membranes such as those formed by lecithin in water were calculated as a function of enclosed volume, membrane area and spontaneous curvature. As the area can be taken to be constant, the only elasticity controlling the shapes of these vesicles is that of curvature. A large variety of rotationally symmetric shapes are presented, allowing for indentations, cavities an...

We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.

We obtain results on the vanishing of divergence of Riemannian and Projective curvature tensors with respect to semi-symmetric metric connection on a trans-Sasakian manifold under the condition φ(gradα) = (n− 2)gradβ.

We consider generators of algebraic covariant derivative curvature tensors R which can be constructed by a Young symmetrization of product tensors W ⊗ U or U ⊗ W , where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2 1). Using Computer Alge...