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On integrability of semi-invariant submanifolds of trans-Sasakian Finsler manifolds. (English) Zbl 1447.58003

Trans-Sasakian manifolds were introduced by J. A. Oubiña [Publ. Math. 32, 187–193 (1985; Zbl 0611.53032)]. The authors introduce the notion of trans-Sasakian Finsler manifold, then study semi-invariant submanifold \(F^m= (\mathcal{Y}, \mathcal{Y}',F)\) of a trans-Sasakian Finsler manifold \(\bar{F}^{2n+1}= (\bar{\mathcal{Y}}, \bar{\mathcal{Y}}', \bar{F})\) and discuss the integrability conditions of the distributions of the semi-invariant submanifolds of the trans-Sasakian Finsler manifold.

MSC:

58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
58A30 Vector distributions (subbundles of the tangent bundles)

Citations:

Zbl 0611.53032
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References:

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