Abstract
In this paper, we introduce semi-invariant semi-Riemannian submersions from para-Kahler manifolds onto semi-Riemannian manifolds. Wegive some examples, investigate the geometry of foliations that arise fromthe de…nition of a semi-Riemannian submersion and check the harmonicity ofsuch submersions. We also find necessary and su¢ cient conditions for a semiinvariant semi-Riemannian submersion to be totally geodesic. Moreover, weobtain curvature relations between the base manifold and the total manifold
Highlights
The theory of Riemannian submersion was introduced by O’Neill and Gray in [19] and [13], respectively
We introduce semi-invariant semi-Riemannian submersions from para-Kähler manifolds onto semi-Riemannian manifolds
We investigate the integrability of the distribution D1 and D2: Since ...bers of semi-invariant semi-Riemannian submersions from para-Kahler manifolds are CR-submanifolds and T is the second fundamental form of the ...bers, we have the following theorem
Summary
The theory of Riemannian submersion was introduced by O’Neill and Gray in [19] and [13], respectively. Riemannian submersions were considered between almost complex manifolds by Watson in [26] under the name of almost Hermitian submersion. He showed that if the total manifold is a Kähler manifold, the base manifold is a Kähler manifold. Riemannian submersions have been considered for quaternionic Kähler manifolds [14] and para-quaternionic Kähler manifolds [4],[15] This kind of submersions have been studied with di¤erent names by many authors (see [1], [10], [12], [21], [22], [23], [24] and more). From a potential function the so-called scalar ...eld on a 2m dimensional locally product manifold called by him strati...ed space
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