Curvature and Differentiable Structure on Spheres
Curvature and symmetry of Milnor spheres.
Curvature contents of geometric spaces.
Curvature, diameter and Betti numbers.
Curvature estimate for the volume growth of globally minimal submanifolds.
Curvature free volume estimates.
Curvature homogeneous riemannian manifolds
Curvature Increasing Metric Variations.
Curvature of the Induced Riemannian Metric on the Tangent Bundle of a Riemannian Manifold.
Curvature on reductive homogeneous spaces.
Curvature operators: pinching estimates and geometric examples
Curvature Pinching and Eigenvalue Rigidity for Minimal Submanifolds.
Curvature Pinching for Odd-dimensional Minimal Submanifolds in a Sphere
Curvature pinching for odd-dimensional minimal submanifolds in a sphere.
Curvature properties of certain compact pseudosymmetric manifolds
Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold
The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, -projectively flat, -projectively flat, --projectively flat, pseudo projectively flat and -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat,...
Curvature tensors and Singer invariants of four-dimensional homogeneous spaces
We show that the Singer invariant of a four-dimensional homogeneous space is at most .
Curvature tensors in dimension four which do not belong to any curvature homogeneous space
A six-parameter family is constructed of (algebraic) Riemannian curvature tensors in dimension four which do not belong to any curvature homogeneous space. Also a general method is given for a possible extension of this result.
Curvature-decreasing maps are volume-decreasing. On joint work with G. Besson and G. Courtois.
Curvatures of the diagonal lift from an affine manifold to the linear frame bundle
We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.