It is well known that an integrable regular H-structure induces on a real manifold Mn the structure of a hypercomplex analytic manifold (h-manifold)\(\mathop M\limits^* _m \). We prove that the Lie derivative of a pure tensor T on Mn is an h-derivative of Lie providing T is h-analytic. With the h-derivative of Lie there is associated on\(\mathop M\limits^* _m \) the hypercomplex derivative of Lie. This enables us to associate to the motions and affine collineations in the Riemannian space\(\mathop V\limits^* _m \) corresponding transformations in a real space Vn.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
G. I. Kruchkovich, “Hypercomplex structures on manifolds, I,” in: Proceedings of the Vector and Tensor Analysis Seminar, Vol. 16 [in Russian] (1972).
K. Yano and S. Bochner, Curvature and Betti Numbers, Ann. of Math. Studies, No. 32, Princeton University Press, Princeton, N.J. (1953).
V. V. Navrozov, “Fundamental concepts of hypercomplex Riemannian geometry,” Trudy MIRÉA, Matematika, No. 67, 50–64 (1973).
G. I. Kruchkovich, “Hypercomplex geodesies and their real realizations,” Trudy MIRÉA, Matematika, No. 67, 3–11 (1973).
Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 603–612, April, 1974.
About this article
Cite this article
Navrozov, V.V. Transformations in hypercomplex Riemannian spaces. Mathematical Notes of the Academy of Sciences of the USSR 15, 356–361 (1974). https://doi.org/10.1007/BF01095128
- Real Space
- Riemannian Space
- Analytic Manifold
- Real Manifold