Geodesic
Spectral Invariants of Affine Hypersurfaces
Publications de l'Institut Mathématique, _N_S_64 (1998) no. 78, p. 133 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
Classification : 53A15 58G25
Keywords: Operators of Laplace type, the Hessian, hypersurface immersed in affine space, the heat equation 
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     author = {Neda Bokan and Peter Gilkey and Udo Simon},
     title = {Spectral {Invariants} of {Affine} {Hypersurfaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {133 },
     publisher = {mathdoc},
     volume = {_N_S_64},
     number = {78},
     year = {1998},
     zbl = {0999.58014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1998_N_S_64_78_a10/}
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Neda Bokan; Peter Gilkey; Udo Simon. Spectral Invariants of Affine Hypersurfaces. Publications de l'Institut Mathématique, _N_S_64 (1998) no. 78, p. 133 . http://geodesic.mathdoc.fr/item/PIM_1998_N_S_64_78_a10/