Global differential invariants of nondegenerate hypersurfaces.
In: Turkish Journal of Mathematics, Jg. 46 (2022-11-01), Heft 6, S. 2208-2230
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Zugriff:
Let {gij(x)}n i,j=1 and {Lij(x)}n i,j=1 be the sets of all coefficients of the first and second fundamental forms of a hypersurface x in Rn+1 . For a connected open subset U Rn and a C 8-mapping x : U Rn+1 the hypersurface x is said to be d-nondegenerate, where d {1, 2, . . . n}, if Ldd(x) 1= 0 for all u U . Let M(n) = {F : Rn -1 Rn | Fx = gx + b, g O(n), b Rn}, where O(n) is the group of all real orthogonal n × n-matrices, and SM(n) = {F M(n) | g SO(n)}, where SO(n) = {g O(n) | det(g) = 1}. In the present paper, it is proved that the set {gij(x),Ldj(x), i, j = 1, 2, . . ., n} is a complete system of a SM(n + 1)-invariants of a d-non-degenerate hypersurface in Rn+1 . A similar result has obtained for the group M(n + 1). [ABSTRACT FROM AUTHOR]
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Global differential invariants of nondegenerate hypersurfaces.
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Autor/in / Beteiligte Person: | SAĞIROĞLU, Yasemin ; GÖZÜTOK, Uğur |
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Zeitschrift: | Turkish Journal of Mathematics, Jg. 46 (2022-11-01), Heft 6, S. 2208-2230 |
Veröffentlichung: | 2022 |
Medientyp: | academicJournal |
ISSN: | 1300-0098 (print) |
DOI: | 10.55730/1300-0098.3264 |
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