EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 64(78), pp. 133--145 (1998)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home

EMIS Home

 		 

SPECTRAL INVARIANTS OF AFFINE HYPERSURFACES

Neda Bokan, Peter Gilkey, Udo Simon

Matemati\v cki fakultet, Beograd, Yugoslavia and Mathematics Department, University of Oregon, Eugene, Oregon 97403, USA and Technische Universitat Berlin, Strasse des 17. Juni 135 D-10623 Berlin, Deutschland

Abstract: Let $M$ be a smooth compact manifold of dimension $m$ with smooth, possibly empty, boundary $\partial M$. If $g$ is a Riemannian metric on $M$ and if $\nabla$ is an affine connection, let $D=D(g,\nabla)$ be the trace of the normalized Hessian; if $\partial M$ is empty, then we impose Dirichlet boundary conditions. The structures $(g,\nabla)$ arise naturally in the context of affine differential geometry and we give geometric conditions which ensure that $D$ is formally self-adjoint in this setting. We study the asymptotics of the heat equation trace; we have that $a_m(D)$ is an affine invariant. We use the asymptotics of the heat equation to study the affine geometry of affine hypersurfaces.

Keywords: Operators of Laplace type, the Hessian, hypersurface immersed in affine space, the heat equation

Classification (MSC2000): 53A15, 58G25

Full text of the article:

Electronic fulltext finalized on: 6 Apr 2000. This page was last modified: 16 Nov 2001.

© 2000 Mathematical Institute of the Serbian Academy of Science and Arts
© 2000--2001 ELibM for the EMIS Electronic Edition