Note on the locally product and almost locally product structures

Nagaraj, Muppinaiya (1967) Note on the locally product and almost locally product structures. In: Proceedings of the Indian Academy of Sciences - Section A, 65 (5). pp. 270-282.

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Abstract

This paper is concerned with a study of some of the properties of locally product and almost locally product structures on a differentiable manifold X n of class C k . Every locally product space has certain almost locally product structures which transform the local tangent space to X n at an arbitrary point P in a set fashion: this is studied in Theorem (2.2). Theorem (2.3) considers the nature of transformations that exist between two co-ordinate systems at a point whenever an almost locally product structure has the same local representation in each of these co-ordinate systems. A necessary and sufficient condition for X n to be a locally product manifold is obtained in terms of the pseudo-group of co-ordinate transformations on X n and the subpseudo-groups [cf., Theoren (2.1)]. Section 3 is entirely devoted to the study of integrable almost locally product structures.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences - Section A
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian Academy of Sciences.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	03 Jun 2010 06:41
Last Modified:	19 Sep 2010 06:06
URI:	http://eprints.iisc.ac.in/id/eprint/27827

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