EINSTEIN EQUATIONS IN LIE ALGEBROIDS
MIHAI ANASTASIEI(1), MANUELA GÎRŢU(2)
1. "Al.I.Cuza" University of Iaşi, Faculty of Mathematics, 700506, Iaşi, Romania and Mathematical Institute "O. Mayer", Romanian Academy, Blvd. Carol I, nr. 8, Iasi, 700506, ROMANIA,
Corresponding author: anastas@uaic.ro
2. "Vasile Alecsandri" University of Bacău, Faculty of Sciences Department of Mathematics, Informatics and Education Sciences Calea Mărăşeşti 157, Bacău 600115, ROMANIA,
Corresponding author: girtum@yahoo.com
Abstract
A Lie algebroid endowed with a Riemannian metric has a canonical connection of Levi-Civita type. We associate to it the Einstein tensor field and using it we construct the Einstein equations. Some particular cases are discussed.