Geodesic
Conformal connection with scalar curvature
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 22-35

Voir la notice de l'article provenant de la source Math-Net.Ru

A conformal connection with scalar curvature is defined as a generalization of a pseudo-Riemannian space of constant curvature. The curvature matrix of such connection is computed. It is proved that on a conformally connected manifold with scalar curvature there is a conformal connection with zero curvature matrix. We give a definition of a rescalable scalar and prove the existence of rescalable scalars on any manifold with conformal connection where a partition of unity exists. It is proved: 1) on any manifold with conformal connection and zero curvature matrix there exists a conformal connection with positive, negative and alternating scalar curvature; 2) on any conformally connected manifold there exists a global gauge-invariant metric; 3) on a hypersurface of a conformal space the induced conformal connection can not be of nonzero scalar curvature.
Keywords: manifold with conformal connection, curvature matrix of connection, gauge transformations, conformal connection with scalar curvature, partition of unity, gauge-invariant metric.
Mots-clés : connection matrix, rescalable scalar 
@article{VUU_2018_28_1_a2,
     author = {L. N. Krivonosov and V. A. Luk'yanov},
     title = {Conformal connection with scalar curvature},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {22--35},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a2/}
}
TY  - JOUR
AU  - L. N. Krivonosov
AU  - V. A. Luk'yanov
TI  - Conformal connection with scalar curvature
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2018
SP  - 22
EP  - 35
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a2/
LA  - ru
ID  - VUU_2018_28_1_a2
ER  - 
%0 Journal Article
%A L. N. Krivonosov
%A V. A. Luk'yanov
%T Conformal connection with scalar curvature
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2018
%P 22-35
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a2/
%G ru
%F VUU_2018_28_1_a2
L. N. Krivonosov; V. A. Luk'yanov. Conformal connection with scalar curvature. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 22-35. http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a2/