Variational problems on contact Riemannian manifolds

Author:
Shukichi Tanno

Journal:
Trans. Amer. Math. Soc. **314** (1989), 349-379

MSC:
Primary 53C15; Secondary 32F25, 58G30

MathSciNet review:
1000553

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Abstract: We define the generalized Tanaka connection for contact Riemannian manifolds generalizing one for nondegenerate, integrable 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-1000553-9

Keywords:
Contact structure,
Tanaka-Webster scalar curvature,
gauge transformation of contact Riemannian structure

Article copyright:
© Copyright 1989
American Mathematical Society