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- Title
Certain infinitesimal transformations on contact metric manifolds.
- Authors
Ghosh, Amalendu
- Abstract
We prove that if a vector field V on a contact metric manifold $${M(\varphi, \xi, \eta, g)}$$ of dimension (2 n+1) leaves the tensor field $${\varphi}$$ invariant, then V is an infinitesimal harmonic transformation. Next, we study contact metric manifolds admitting a vector field V that leaves the structure tensor $${\varphi}$$ invariant and satisfies different conditions, namely (1) $${Q\varphi = \varphi Q}$$ , (2) M is Jacobi $${(k, \mu)}$$ -contact manifold, (3) $${R(X, Y)\xi = 0}$$ , for any vector fields X, Y orthogonal to $${\xi}$$ and (4) $${\pounds_{V}C = 0}$$ , where C is the conformal curvature tensor.
- Subjects
INFINITESIMAL transformations; CONTACT manifolds; MATHEMATICAL proofs; VECTOR fields; DIMENSIONS
- Publication
Journal of Geometry, 2015, Vol 106, Issue 1, p137
- ISSN
0047-2468
- Publication type
Article
- DOI
10.1007/s00022-014-0240-4