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Point Correspondences between N + 1 Hypersurfaces of Projective Spaces and (N + 1)-Webs

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DOI: 10.4236/am.2013.411A4003    3,323 Downloads   4,350 Views   Citations
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ABSTRACT

For a correspondence in question we establish a sequence of fundamental geometrical objects of the correspondence and find invariant normalizations of the first and second orders of all hupersurfaces under the correspondence. We single out main tensors of the correspondence and establish a connection between the geometry of point correspondences between n + 1 hypersurfaces of projective spaces and the theory of multidimensional (n + 1)-webs.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

V. Bolodurin, "Point Correspondences between N + 1 Hypersurfaces of Projective Spaces and (N + 1)-Webs," Applied Mathematics, Vol. 4 No. 11D, 2013, pp. 14-22. doi: 10.4236/am.2013.411A4003.

References

[1] V. V. Ryzhkov, “Differential Geometry of Point Correspon-dences between Spaces, Itogi Nauki, Geometry,” VINITI Akademii Nauk SSSR, 1965, pp. 65-107.
[2] A. Svec, “Quelques Problems de la Geometrie Differetielle Affine et Proejektive des Correspondances Entre les Surfaces,” Czecho-slavakian Mathematical Journal, Vol. 6, No. 81, 1956, pp. 177-189.
[3] L. Muracchini, “Tranformazioni Puntuali Fra Spazi Conformi e Connessioni Conformi,” Bollettino della Unione Matematica Italiana, Vol. 17, No. 2, 1962, pp. 191-198.
[4] T. Mihailescu, “Geometrie Differentiala Projectiva,” Teoria Corespondentei, Edit. Acad. R.P.R, 1963.
[5] G. Vranceanu, “Tranformazioni Puntuali Fra Spazi Affini o Projettivi e Spazi a Connessione Affine Euclidea,” Bollettino della Unione Matematica Italiana, Vol. 12, No. 2, 1957, pp. 145-153.
[6] V. V. Ryzhkov, “Characteristic Directions of Point Mapping into ,” VINITI Akademii Nauk SSSR, Trudy Geometricheskogo Seminara, Vol. 3, 1971, pp. 235-242.
[7] T. A. Sokolova, “On Question of Point Correspondences of Three Projective Spaces,” VINITI Akademii Nauk SSSR, Trudy Geometricheskogo Seminara, Vol. 4, 1973, pp. 269-283.
[8] J. V. Pavljuchenko, “About Characteristic System of Point Correspondences,” VINITI Akademii Nauk SSSR, Trudy Geometricheskogo Seminara, Vol. 3, 1971, pp. 221234.
[9] A. P. Norden, “Spaces of an Affine Connection,” GITTL, 1950.
[10] N. M. Ostinay, “Geometry of a Multidi-mensional Surface of Projective Space,” VINITI Akademii Nauk SSSR, Trudy Geometricheskogo Seminara, Vol. 1, 1966, pp. 239-263.
[11] M. A. Akivis, “Three-Webs of Multidimensional Surfaces,” VINITI Akademii Nauk SSSR, Trudy Geomet-richeskogo Seminara, Vol. 2, 1969, pp. 7-31.
[12] V. S. Bolodurin, “Projective-Differential Properties of Point Corre-spondences between Three Hypersurfaces,” Izvestiya Vysshikh Uchebnykh Zavedenii, Matematika, Vol. 12, 2012, pp. 16-29.
[13] V. S. Bolodurin, “On the Invarient Theory of Point Correspondences of Three Projective Spaces,” Izvestiya Vysshikh Uchebnykh Zavedenii, Matematika, Vol. 5, 1982, pp. 8-15.
[14] V. V. Goldberg, “On (n + 1)-Webs of Multidimen-sional Surfaces,” Doklady Akademii Nauk SSSR, Vol. 210, No. 4, 1973, pp. 756-759.
[15] G. F. Laptev, “Invariant Construction of Projective Differential Geometry of Surface,” Doklady Akademii Nauk SSSR, Vol. 2, 1949, pp. 121-124.
[16] G. Casanova, “La Notion de Pole Harmonique,” Rev. Math. Spec, Vol. 65, No. 6, 1955, pp. 437-440.

  
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