Fereshteh MALEK, Niloufar HOSSEINPOUR KASHANI

Conformal changes of generalized paracontact pseudometric structures

We characterize generalized almost paracontact pseudometric structures after a conformal change andinvestigate invariant components of these structures under conformal changes. Then we characterize the conformalchanges of normal generalized paracontact pseudometric structures, generalized almost para-co-Kähler structures, andgeneralized para-co-Kähler structures. We also give examples of a generalized almost para-co-Kähler structure and anormal generalized paracontact pseudometric structure that remains invariant under a nonhomothety conformal change.

PDF

___

[1] Blair D. Riemannian Geometry of Contact and Symplectic Manifolds. New York, NY, USA: Birkhauser, 2002.
[2] Gualtieri M. Generalized complex geometry. Annals of Mathematics 2011; 174 (1): 75-123.
[3] Hitchin J. Generalized Calabi Yau manifolds. Quarterly Journal of Mathematics 2003; 54: 281-308.
[4] Kashani NH, Malek F. Generalized para-coKähler structures. Scientific Annals of the Alexandru Ioan Cuza University of Iaşi (New Series) (in press).
[5] Matsuzoe H. Geometry of semi-Weyl manifolds and Weyl manifolds. Kyushu Journal of Mathematics 2001; 55: 107-117.
[6] Poon YS, Wade A. Generalized contact structures. Journal of London Mathematical Society 2011; 83: 333-352.
[7] Sahin B, Sahin F. Generalized almost para-contact structures. International Journal of Geometric Methods in Modern Physics 2017; 14: 1-21.
[8] Vaisman I. Lectures on the Geometry of Poisson Manifolds. Progress in Mathematics, Vol. 118. Basel, Switzerland: Birkhauser, 1994.
[9] Vaisman I. Conformal changes of generalized complex structures. Scientific Annals of the Alexandru Ioan Cuza University of Iaşi (New Series) 2008; 54: 1-14.
[10] Vaisman I. From generalized Kähler to generalized Sasakian structures. Journal of Geometry and Symmetry in Physics 2010; 18: 63-86.
[11] Vaisman I. Generalized para-Kähler manifolds. Differential Geometry and Its Applications 2015; 42: 84-103.