Abstract
For the Grassman-like manifold of centered planes in a projective space, we construct an object, which is the tensor of nonabsolute displacements. If this tensor vanishes, then parallel displacements of clothing planes are absolute.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. O. Belova, “Connection in the fibering associated with Grassman-like manifold of centered planes,” Vestn. Chuvash. Pedagogical Univ., No. 5 (52), 18–20 (2006).
O. O. Belova, “Curvature tensor of connection in the fibering over Grassman-like manifold of centered planes,” Differ. Geom. Mnogoobr. Figur, 40, 18–28 (2009).
L. E. Evtushik, Yu. G. Lumiste, N. M. Ostianu, and A. P. Shirokov, “Differential-geometric structures on the manifolds,” Itogi Nauki Tekh. Ser. Probl. Geom. Tr. Geom. Sem., 9, 5–246 (1979).
A. P. Norden, Spaces with Affine Connection [in Russian], Nauka, Moscow (1976).
Yu. I. Shevchenko, Clothings of Centroprojective Manifolds [in Russian], Kaliningrad (2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 3–5, 2010.
Rights and permissions
About this article
Cite this article
Belova, O.O. Tensor of nonabsolute displacements on Grassman-like manifold of centered planes. J Math Sci 177, 647–648 (2011). https://doi.org/10.1007/s10958-011-0491-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-011-0491-7