THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY

Title & Authors
THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY
Park, Jeong-Hyeong;

Abstract
Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\small{\Delta}$$\small{_{p}}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\small{\Delta}$$\small{_{p}}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.
Keywords
totally umbillic boundary;totally geodesic boundary;minimal boundary;absolute boundary conditions;relative boundary conditions;Dirichlet Laplacian;Neumann Laplacian.;
Language
English
Cited by
1.
Spectral geometry of eta-Einstein Sasakian manifolds, Journal of Geometry and Physics, 2012, 62, 11, 2140
2.
Multi- C ∗ \$C^{*}\$ -ternary algebras and applications, Journal of Inequalities and Applications, 2015, 2015, 1
References
1.
T. Branson and P. Gilkey, The asymptotics of the Laplacian on a manifold with boundary, Comm. Partial Differential Equations 15 (1990), 245–272

2.
P. B. Gilkey, Asymptotic Formulae in Spectral Geometry, CRC Press, 2003

3.
V. K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970), 269–285

4.
J. H. Park, Spectral geometry and the Kaehler condition for He rmitian manifolds with boundary, Contemp. Math. 337 (2003) AMS, 121–128

5.
R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Math. 10 (1968), 288–307

6.
R. T. Seeley, Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math. 91 (1969), 963–983