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Geometry of manifolds which admit conservation laws

David E. BlairAlexander P. Stone — 1971

Annales de l'institut Fourier

Let M be an ( n + 1 ) -dimensional Riemannian manifold admitting a covariant constant endomorphism h of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that M is locally flat, a manifold N immersed in M is studied. The manifold N has an induced structure with n of the same eigenvalues if and only if the normal to N is a fixed direction of h . Finally conditions under which N is invariant under h , N is totally geodesic and the induced structure has vanishing Nijenhuis...

Conformal and related changes of metric on the product of two almost contact metric manifolds.

David E. BlairJosé Antonio Oubiña — 1990

Publicacions Matemàtiques

This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, α-Sasakian and β-Kenmotsu structures.

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