论文信息 - Variational problems on contact Riemannian manifolds

Variational problems on contact Riemannian manifolds

We define the generalized Tanaka connection for contact Riemannian manifolds generalizing one for nondegenerate, integrable CR manifolds. Then the torsion and the generalized Tanaka-Webster scalar curvature are defined properly. Furthermore, we define gauge transformations of contact Riemannian structure, and obtain an invariant under such transformations. Concerning the integral related to the invariant, we define a functional and study its first and second variational formulas. As an example, we study this functional on the unit sphere as a standard contact manifold.

Shukichi Tanno | S. Tanno

[1] David E. Blair,et al. Contact manifolds in Riemannian geometry , 1976 .

[2] D. Blair. Critical associated metrics on contact manifolds. II , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[3] S. Tanno. Harmonic forms and Betti numbers of certain contact Riemannian manifolds , 1967 .

[4] S. Tanno. The topology of contact Riemannian manifolds , 1968 .

[5] Noboru Tanaka,et al. On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections , 1976 .

[6] S. Sasaki. ON DIFFERENTIABLE MANIFOLDS WITH CERTAIN STRUCTURES WHICH ARE CLOSELY RELATED TO ALMOST CONTACT STRUCTURE I , 1960 .

[7] THE FIRST EIGENVALUE OF THE LAPLACIAN ON SPHERES , 1979 .

[8] John M. Lee,et al. The Yamabe problem on CR manifolds , 1987 .

[9] N. Tanaka. On the pseudo-conformal geometry of hypersurfaces of the space of $n$ complex variables , 1962 .

[10] S. M. Webster,et al. Pseudo-Hermitian structures on a real hypersurface , 1978 .

[11] S. Chern,et al. On riemannian metrics adapted to three-dimensional contact manifolds , 1985 .

[12] John M. Lee,et al. Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem , 1988 .

[13] S. Webster. On the pseudo-conformal geometry of a Kähler manifold , 1977 .