Showing papers in "Annals of Global Analysis and Geometry in 1991"

Théorème de De Rham pour les variétés stratifées

Abstract: oindent {\bf Theoreme de De Rham. } Soit A une prestratification abstraite, et $(\bar{{\rm p}}, \bar{{\rm q}})$ deux perversites complementaires; le morphisme d'integration induit un isomorphisme entre la coho\-mo\-lo\-gie du complexe $\Omega^{*}_{\bar{{\rm q}}}({\rm A})$ des formes differentielles d'inter\-sec\-tion et la coho\-mo\-lo\-gie d'inter\-sec\-tion ${\rm IH^{*}_{\bar{p}}(A, I \! R)}$.

Upper Bounds of small Eigenvalues of the Dirac Operator and Isometric immersions

Abstract: We show that a topologically determined number of eigenvalues of the Dirac operatorD of a closed Riemannian spin manifoldM of even dimensionn can be bounded by the data of an isometric immersion ofM into the Euclidian spaceR N . From this we obtain similar bounds of the eigenvalues ofD in terms of the scalar curvature ofM ifM admits a minimal immersion intoS N or,ifM is complex, a holomorphic isometric immersion intoPC N .

On spectral flow of transversal dirac operators and a theorem of Vafa-Witten

Abstract: We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of a family of transversal Dirac operators relative to a Riemannian foliation. The family in question is parameterized by a moduli space of basic connections with respect to the foliation modulo a suitable group of foliation preserving gauge transformations. The proof is based on the concept of spectral flow, applied to the suspension of suitable gauge transformations to periodic families of Dirac operators.

Existence of codimension one foliations with minimal leaves

Abstract: Every smooth closed manifold of dimension 4 or greater that has a smooth codimension one foliation, has such aC1 foliation whose leaves are minimal hypersurfaces for someC1 Riemannian metric.

Locally symmetric and ricci-symmetric contact metric manifolds

Abstract: We have characterized locally symmetric and Ricci-symmetric contact metric manifolds of dimension greater than 3, by assuming certain conditions on the curvature and Ricci curvature along the characteristic vector field of the contact structure.

Symplectic reflections and complex space forms

Abstract: We prove that a Hermitian manifold is a complex space form if and only if the local reflections with respect to any holomorphic surface are symplectic, i.e., preserve the Kahler form.

On Square Integrability of Mean Curvature for Surfaces with Positive Gaussian Curvature

Abstract: We show that {ie319-1} H2dµ = ∞ for any complete surface M ⊂ R3 which has positive curvature outside a compact subset of R3. This proves a conjecture of Friedrich.

A family of metrics on the moduli space of BPST-instantons

Abstract: A family {g s} s≧0 of Riemannian metrics on the moduli space of BPST-instantons is considered. Explicit expressions of g s are given and conclusions concerning the geometry of the instanton space are deduced.

Bundle functors on Fibred manifolds

Abstract: We give a proof of the regularity of bundle functors on a certain class of categories over manifolds and a description of all bundle functors on fibred manifolds with fixed dimensions of bases and fibres. Further, we describe in the terms of Weil algebras all bundle functors on fibred manifolds with fixed dimensions of bases preserving fibred products. Finally we discuss certain natural operations with vector fields. In this paper, all manifolds are smooth and paracompact. We denote byN 0 the set of all non-negative integers.

Generalized Jacobians and rigidificators

Abstract: The purpose of this paper is to give a new interpretation and generalization of both the singularization procedure of Rosenlicht and the concept of the generalized Jacobian [18], which arose in the attempt to understand the role the generalized Jacobian plays in Krichever's theory of the integration of non-linear evolution equations in terms of theta functions of curves [14], [16]. The interpretation of the generalized Jacobian as a rigidificator for the Jacobian of a regular curve is not surprising (cf. Drinfeld [3]), but does not seem to exist in the present literature on algebraic curves.

Twistor theory and Blaschke manifolds

Abstract: Using the twistor theory on quaternionic Kaehler manifolds and some recent results on Blaschke manifolds and compact manifolds whose holonomy group is Spin (7), we prove that a Blaschke manifold of nonnegative scalar curvature whose holonomy group is exceptional is isometric to a projective space.