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Paraquaternionic CR-Submanifolds

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Geometry of Cauchy-Riemann Submanifolds

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.

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Acknowledgments

The author was supported by CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0118.

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Authors and Affiliations

  1. Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, Ploieşti, 100680, Romania

    Gabriel-Eduard Vîlcu

  2. Faculty of Mathematics and Computer Science, University of Bucharest, Research Center in Geometry, Topology and Algebra, Str. Academiei 14, Sector 1, Bucureşti, Bucharest, 70109, Romania

    Gabriel-Eduard Vîlcu

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  1. Gabriel-Eduard Vîlcu
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Correspondence to Gabriel-Eduard Vîlcu .

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Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Potenza, Italy

    Sorin Dragomir

  2. Dept. of Maths., Faculty of Natural Sci, Jamia Millia Islamia,, New Delhi, Delhi, India

    Mohammad Hasan Shahid

  3. Department of Mathematics, King Abdul Aziz University, Thuwal, Saudi Arabia

    Falleh R. Al-Solamy

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Vîlcu, GE. (2016). Paraquaternionic CR-Submanifolds. In: Dragomir, S., Shahid, M., Al-Solamy, F. (eds) Geometry of Cauchy-Riemann Submanifolds. Springer, Singapore. https://doi.org/10.1007/978-981-10-0916-7_13

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