Tangent bundle of the hypersurfaces in a Euclidean space.
Tangent sphere bundles of natural diagonal lift type.
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...
The Classification of ...-symmetric Sasakian Manifolds.
The Closed Geodesics of a Special Manifold.
The Cut Locus of Noncompact Finitely Connected Surfaces Without Conjugate Points
The Dirac operator on collapsing -bundles
The Dolbeault operator on Hermitian spin surfaces
We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.
The eta invariant and metrics of positive scalar curvature.
The Evolution of the Weyl Tensor under the Ricci Flow
We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.
The explicit construction of Einstein Finsler metrics with non-constant flag curvature.
The f-sectional curvature of f-Kaehlerian manifolds
The geometry and topology of 3-Sasakian manifolds.
The L2-Structure of Moduli spaces of Einstein Metrics on 4-Manifolds.
The laplacian on asymptotically flat manifolds and the specification of scalar curvature
The local moduli of Sasakian 3-manifolds.
The Schläfli formula in Einstein manifolds with boundary.
The Schouten-van Kampen Affine Connections Adapted to Almost (Para)Contact Metric Structures
The Soliton-Ricci Flow with variable volume forms
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation. This gauge is generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times. It represents the gradient flow of...
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...