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Selfadjoint Metrics on Almost Tangent Manifolds Whose Riemannian Connection is Almost Tangent

Published online by Cambridge University Press:  20 November 2018

D. S. Goel
D. S. Goel*
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Canada
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Let M be a differentiable manifold of class C∞, with a given (1, 1) tensor field J of constant rank such that J2=λI (for some real constant λ). J defines a class of conjugate (G-structures on M. For λ>0, one particular representative structure is an almost product structure. Almost complex structure arises when λ<0. If the rank of J is maximum and λ=0, then we obtain an almost tangent structure. In the last two cases the dimension of the manifold is necessarily even. A Riemannian metric S on M is said to be related if one of the conjugate structures defined by S has a common subordinate structure with the G-structure defined by S. It is said to be J-metric if the orthogonal structure defined by S has a common subordinate structure.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 671 - 674
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Clark, R. S. and Goel, D. S., On the geometry of an almost tangent manifold, Tensor, 24 (1972) pp. 243–252.Google Scholar
2. Goel, D. S., Almost tangent structures Ph.D. thesis 1972, University of Calgary.Google Scholar
3. Yano, K. and Kobayashi, S., Prolongation of tensor fields and connections to tangent bundles I, J. Math. Soc. Japan 18 (1966), pp. 194–210.Google Scholar