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JOURNALS // Proceedings of the Yerevan State University, series Physical and Mathematical Sciences // Archive

Proceedings of the YSU, Physical and Mathematical Sciences, 1990 Issue 2, Pages 37–42 (Mi uzeru804)

Mathematics

Fully geodetic surfaces in Riman orthogonal composition spaces

L. Syaotzin, L. A. Matevosyan

Yerevan State University

Abstract: The surfaces $X_m=X_{m_1}+X_{m_2}$ are considered in Riman space $V_n$ admitting two multiform compositions with fully orthogonal transversal positions $V_{n_1}$ and $V_{n_2}$, where $X_{m_1}$ is fully geodetic surface in $V_{n_1}$ and $X_{m_2}$ f.g.s. in $V_{n_2}$. The basic values of surface $X_m$ have also been found and the following statement is proved: in order all the surfaces be completely geodetic, it is necessary and sufficient $V_n$ being reduced space.

UDC: 514.764

Received: 08.12.1989
Accepted: 20.07.1990



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