پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 499 |
| تعداد مقالات | 4,441 |
| تعداد مشاهده مقاله | 7,673,938 |
| تعداد دریافت فایل اصل مقاله | 5,166,549 |
Hypersurfaces in the general inner product spaces | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 1، شهریور 2017، صفحه 17-27 اصل مقاله (310.69 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2658 | ||
| نویسنده | ||
| Ali Parsian* | ||
| Department of Mathematics, Tafresh University, Tafresh 39518 79611, Iran | ||
| چکیده | ||
| Let A be a symmetric positive definite (n+ 1)×(n+ 1) real matrix for n ≥ 1 and S ∈ R n+1 be a hypersurface. We are supposed to determine the tangent space TpS in an arbitrary point p ∈ S in the case that the whole space R n+1 admits the inner product with matrix A. Among other things, some maximum and minimum properties for the vector fields perpendicular to tangent spaces of hypersurfaces, the compatibility of the image or inverse image of a hypersurface and its tangent space under an embedding, an isometry, and a submersion are also pointed out. | ||
| کلیدواژهها | ||
| Hypersurface؛ Integral curve؛ Vector field | ||
| مراجع | ||
|
[1] A. V. Arutyunov, and A. F. Izmailov, Tangent vectors to a zero set at abnormal points,J. Math.Anal.Appl.,289(2004),66–76. [2] N. A. Baas, On higher structures, International Journal of General Systems, 45 (6), (2016), 747–762. [3] R. A. Beezer, A first course in linear algebra, Washington: University of Puget Sound (2010). [4] P. Corsini, and V. Leoreanu, Applications of hyperstructure theory, Dordrecht, the Netherlands: Kluwer Academic Publisher (2003). [5] P. Corsini, History and new possible research directions of hyperstructures, Ratio Mathematica, 21, (2011), 3–26. [6] P. Corsini and V. Leoreanu, On the grade of a sequence of fuzzy sets and join spaces determined by a hypergraph, Southeast Asian Bull. Math., 34 (2010) 231–242. [7] M. do Carmo, Differential geometry of curves and surfaces, New Jersey: Prentice Hall (1977). [8] Y. Feng, Algebraic hyperstructures obtained from algebraic structures with fuzzy binary relations, Italian J. Pure Appl. Math., 25 (2009) 157–164. [9] Y. Feng, Y. Jiang and V. Leoreanu, On the grade of sequence of fuzzy sets and join spaces determined by a hypergraph II, Afr. Mat., 24 (2013) 83–91. [10] Y. Feng, Q. Zeng and H. Duan, On (λ; µ)-fuzzy subhyperlattices, Italian J. Pure Appl. Math., 30 (2013), 79–86. [11] T. Frankel, The Geometry of physics, Cambridge: Cambridge University Press (2012). [12] W. Hurewicz, Lectures on ordinary differential equations, Cambridge: M. I. T. Press, Dover ed. (2014). [13] V. Lakshmibai, On tangent spaces to Schubert varieties, Journal of Algebra, 224 (2000), 167–197. [14] V. Lakshmibai, On tangent spaces to Schubert varieties, Journal of Algebra, 230 (2000), 244–224. [15] V. Leoreanu and L. Leoreanu, Hypergroups associated with hypergraphs, Italian J. Pure Appl. Math., 4 (1998), 119–126. [16] J. Milnor, Topology from the differential viewpoint, Charlottesville: The Univer-sity Press of Virginia (1972). [17] P. Polo, On Zariski tangent spaces of Schubert varieties, and a proof of a con-jecture of Deodhar, Indag. Mathem., N.S., 5(4) (1994), 483–493. [18] M. Spivak, A comprehensive introduction to differential geometry, Vol. 1, New York: Publish or Perish Inc. (1975). [19] R. H. Wasserman, Tensors and manifolds, New York: Oxford University Press (1992). [20] G. Zeng, Determination of the tangents for a real plane algebraic curve, Journal of Symbolic Computation, 41 (2006), 863–886. | ||
|
آمار تعداد مشاهده مقاله: 411 تعداد دریافت فایل اصل مقاله: 735 |
||