Search results for "Ricci-flat manifold"

Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds

2012

Abstract We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Homeomorphic graph manifolds: A contribution to the μ constant problem

1999

Abstract We give a characterization, in terms of homological data in covering spaces, of those maps between (3-dimensional) graph manifolds which are homotopic to homeomorphisms. As an application we give a condition on a cobordism between graph manifolds that guarantees that they are homeomorphic. This in turn is applied to give a partial result on the μ -constant problem in (complex) dimension three.

Some remarks on minimal surfaces in riemannian manifolds

1970

On cobordism of manifolds with corners

2000

This work sets up a cobordism theory for manifolds with corners and gives an identication with the homotopy of a certain limit of Thom spectra. It thereby creates a geometrical interpretation of Adams-Novikov resolutions and lays the foundation for investigating the chromatic status of the elements so realized. As an application Lie groups together with their left invariant framings are calculated by regarding them as corners of manifolds with interesting Chern numbers. The work also shows how elliptic cohomology can provide useful invariants for manifolds of codimension 2.

Three physical quantum manifolds from the conformal group

1987

Heat semi-group and generalized flows on complete Riemannian manifolds

2011

Abstract We will use the heat semi-group to regularize functions and vector fields on Riemannian manifolds in order to develop Di Perna–Lions theory in this setting. Malliavinʼs point of view of the bundle of orthonormal frames on Brownian motions will play a fundamental role. As a byproduct we will construct diffusion processes associated to an elliptic operator with singular drift.

Real quadrics in C n , complex manifolds and convex polytopes

2006

In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…

Star calculus on Jacobi manifolds

2002

Abstract We study the Gerstenhaber bracket on differential forms induced by the two main examples of Jacobi manifolds: contact manifolds and l.c.s. manifolds. Moreover, we obtain explicit expressions of the generating operators and the derivations on the algebra of multivector fields. We define star operators for contact manifolds and l.c.s. manifolds and we study some of its properties.

Linear invariants of Riemannian almost product manifolds

1982

Using the decomposition of a certain vector space under the action of the structure group of Riemannian almost product manifolds, A. M. Naveira (9) has found thirty-six distinguished classes of these manifolds. In this article, we prove that this decomposition is irreducible by computing a basis of the space of invariant quadratic forms on such a space.

Complex powers on noncompact manifolds and manifolds with singularities

1988