Generalized metric and gravity

Abstract

Na zklade znalost z diferencilnej geometrie je predstaven zoveobecnen geometria. V dsledku symetri tejto novej geometrie sa prirodzene vynra B-pole znme z terie strn. Taktie bola zkontruovan zoveobecnen metrika pozostvajca z klasickej metriky a u spomnanho B-poa. Hore uveden truktry umouj zavies konexiu na zoveobecnenej geometrii a rozvin Riemannovsk zoveobecnen geometriu. Nahradenm obyajnej krivosti za zoveobecnen v Einstein-Hilbertovej akcii dostvame akciu npadne podobn boznovej asti akcie supergravitcie.

Based on the knowledge from differential geometry, the generalized geometry is introduced. As a consequence of the symmetries in this new geometry, a B-field, known from the string theory, inherently emerges. Generalized metric based on ordinary metric tensor and the B-field will be established as well. This allows to construct connection in the framework of generalized geometry and develop a Riemannian generalized geometry. From this point, it is a straightforward way to the replacement of an ordinary scalar curvature by the generalized one in Einstein-Hilbert action. Obtained action closely resembles the supergravity action, especially the bosonic part.