Lorentzian Geometry and CR-Submanifolds

Krishan L. Duggal ()
Additional contact information
Krishan L. Duggal: University of Windsor, Department of Mathematics and Statistics

Chapter Chapter 6 in Geometry of Cauchy-Riemann Submanifolds, 2016, pp 151-177 from Springer

Abstract: Abstract This paper contains an up-to-date information on the Lorentzian geometry of CR-submanifolds, contact CR-submanifolds and globally framed CR-submanifolds (M, g) of an indefinite semi-Riemannian manifold. In view of the large number of excellent paper appearing in this field, we focus on those key results whose Lorentzian geometry is different than their corresponding Riemannian geometry. Contrary to the case of Riemannian CR-submanifolds and above-stated two other classes, the induced distribution D of M, has three subcases, namely, (a) $$g_{|D}$$ g | D is spacelike or (b) $$g_{|D}$$ g | D is Lorentzian or (c) $$g_{|D}$$ g | D is lightlike. For the first two subcases D is an invariant submanifold of M, but, the third subcase need not be invariant. We notice that the geometry of the subcase (a) is mostly similar with the Riemannian case, but, the subcase (b) still remains an open problem since $$g_{|D}$$ g | D Lorentzian is not compatible with the required Hermitian structure of D. Moreover, the geometry of subcase (c) is quite different for which we provide several new results. We also give interesting physical examples used in relativity.

Keywords: Lorentzian manifold; CR-structure; CR-submanifold; Indefinite Kähler manifold; Contact CR-submanifold; Globally framed structure; 53C50; 53C55; 83C50 (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-0916-7_6

Ordering information: This item can be ordered from
http://www.springer.com/9789811009167

DOI: 10.1007/978-981-10-0916-7_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().