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Weitzenböck formula for SL(q)-foliations

Bartoszek A., Kalina J., Pierzchalski A.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 2

179-188

A Weitzenböck formula for SL(q)-foliations is derived. Its linear part is a relative trace of the relative curvature operator acting on vector valued forms.

On D-homothetic deformation of trans-Sasakian structure

Shaikh A., Baishya K., Eyasmin S.

Demonstratio Mathematica

2008

Vol. 41, nr 1

171-188

The object of the present paper is to study a transformation called D-homothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor phi and the operator Qphi - phiQ is conformal under a D-homothetic deformation. Also the phi-sectional curvature of a trans-Sasakian manifold is conformal under such a deformation. Some non-trivial examples of trans-Sasakian (non-Sasakian) manifolds with global vector fields are obtained.