On a Riemannian Manifold M 2n with an Almost Tangent Structure

1 January 1969

journal article
Published by Canadian Mathematical Society in Canadian Mathematical Bulletin

Vol. 12 (6) , 759-769
https://doi.org/10.4153/cmb-1969-098-1

Abstract

Professor Eliopoulous studied almost tangent structures on manifolds M_2n in [1; 2]. An almost tangent structure F is a field of class C^∞ of linear operations on M_2n such that at each point x in M_2n, F_x maps the complexified tangent space into itself and that F_x is of rank n everywhere and satisfies that F² = 0. In this note, we consider a (1,1) tensor field . on a Riemannian M_2n which satisfies everywhere and is such that the rank of F is n everywhere. Such gives an almost tangent structure F on M_2n.

Keywords

This publication has 3 references indexed in Scilit:

On the General Theory of Differentiable Manifolds with Almost Tangent Structure
Canadian Mathematical Bulletin, 1965
On some structures which are similar to the quaternion structure
Tohoku Mathematical Journal, 1960
Affine connexions in an almost product space
Kodai Mathematical Journal, 1959