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Semi-invariant submersions whose total manifolds are locally product Riemannian

Fatma Ozdemir
Cem Sayer
Hakan Mete Tastan


We study Riemannian and semi-invariant submersions whose total man-ifolds are locally product Riemannian. The necessary and sufficient conditions for the integrability and totally geodesicness of all distributions which are introduced in the denition of the semi-invariant submersion are obtained. We also give a charac- terization theorem for the proper semi-invariant submersions with totally umbilical fibers and find some results for such submersions with parallel canonical structures. Moreover, we define first variational formula on the fibers of a semi-invariant sub-mersion and by the virtue of that we prove a new theorem which has a condition for the harmonicity of a semi-invariant submersion.

Mathematics Subject Classication (2010): Primary 53C15, 53B20.

Key words: Riemannian submersion, semi-invariant submersions, horizontal distribution fiber, locally product Riemannian manifold, rst variational formula.

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eISSN: 1727-933X
print ISSN: 1607-3606