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Paraquaternionic CR-Submanifolds

In: Geometry of Cauchy-Riemann Submanifolds

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  • Gabriel-Eduard Vîlcu

    (Petroleum-Gas University of Ploieşti
    University of Bucharest, Research Center in Geometry, Topology and Algebra, Faculty of Mathematics and Computer Science)

Abstract

Paraquaternionic structures, at first known as quaternionic structures of second kind, are due to P. Libermann. Their study parallels that of quaternionic manifolds, yet relies on the algebra of paraquaternionic numbers. The counterpart in odd dimension of a paraquaternionic structure was introduced in 2006 by S. Ianuş, R. Mazzocco and G.E. Vîlcu and is referred to as a mixed 3-structure. It appears in a natural way on lightlike hypersurfaces in paraquaternionic manifolds. In this paper we review basic results concerning several types of submanifolds and semi-Riemannian submersions of manifolds endowed with paraquaternionic and mixed 3-structures.

Suggested Citation

  • Gabriel-Eduard Vîlcu, 2016. "Paraquaternionic CR-Submanifolds," Springer Books, in: Sorin Dragomir & Mohammad Hasan Shahid & Falleh R. Al-Solamy (ed.), Geometry of Cauchy-Riemann Submanifolds, chapter 0, pages 361-390, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-0916-7_13
    DOI: 10.1007/978-981-10-0916-7_13
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