Variational problems on contact Riemannian manifolds

Tanno, Shukichi

doi:10.1090/S0002-9947-1989-1000553-9

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ISSN 1088-6850(online) ISSN 0002-9947(print)

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 ${\text{CR}}$ 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.

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