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Wani, Towseef Ali; Lone, Mehraj Ahmad

Horizontally conformal submersions from CR-submanifolds of locally conformal quaternionic Kähler manifolds. (Horizontally conformal submersions from CR-submanifolds of locally conformal quaternionic Kaehler manifolds.) (English) Zbl 1492.53078

Mediterr. J. Math. 19, No. 3, Paper No. 114, 12 p. (2022).
Summary: In this paper, we study the horizontally conformal submersions of CR-submanifols of locally conformal quaternion Kaehler manifolds. We prove that any horizontal homothetic submersion of a CR-submanifold \(M\) of a locally conformal quaternion Kaehler manifold with Lee vector field normal to \(M\) is a Riemannian submersion up to a scale. Moreover, if \(M\) is mixed geodesic then such a map is harmonic. This paper extends the results obtained by B. Sahin [Kodai Math. J. 31, No. 1, 46–53 (2008; Zbl 1138.53031)] and G.-E. Vîlcu [Mediterr. J. Math. 17, No. 1, Paper No. 26, 13 p. (2020; Zbl 1433.53051)] to locally conformal quaternion Kaehler manifolds.

Cited in 6 Documents

MSC:

53C40 Global submanifolds
32V40 Real submanifolds in complex manifolds
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C55 Global differential geometry of Hermitian and Kählerian manifolds

Keywords:

locally conformal quaternion Kähler manifold; quaternion CR-submanifold; Riemannian submersion

Citations:

Zbl 1138.53031; Zbl 1433.53051
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Full Text: DOI

References:

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