SEMIPARALLEL TENSOR PRODUCT SURFACES IN E^4

Year 2014, Volume: 7 Issue: 1, 36 - 43, 30.04.2014

Betül Bulca , Kadri Arslan

https://doi.org/10.36890/iejg.594494

Abstract

Keywords

Normal curvature, Tensor product surface, Semiparallel surface

References

• [1] Arslan, K. and Murathan, C., Tensor Product Surfaces of Pseudo-Euclidean Planar Curves, Geometry and Topology of Submanifolds, VII, World Scientific, (1994), 71-75.
• [2] Chen,B.Y., Geometry of Submanifolds, Dekker, New York, 1973.
• [3] Chen, B.Y., Differential Geometry of Semiring of Immersions, I:General Theory, Bull. Inst. Math. Acad. Sinica, 21(1993),1-34.
• [4] Decruyenaere, F., Dillen, F., Mihai, I., Verstraelen, L., Tensor Products of Spherical and Equivariant Immersions, Bull. Belg. Math. Soc. - Simon Stevin, 1(1994), 643-648.
• [5] Decruyenaere, F., Dillen, F., Verstraelen, L., Vrancken, L., The Semiring of Immersions of Manifolds, Beitrage Algebra Geom. 34(1993), 209-215.
• [6] Deprez, J., Semi-parallel Surfaces in Euclidean Space, J. Geom., 25(1985), 192-200.,
• [7] Deszcz, R., On Pseudosymmetric Spaces, Bull. Soc. Math. Belg., 44 ser. A, (1992), 1-34.
• [8] Ferus, D., Symmetric Submanifolds of Euclidean Space, Math. Ann., 247(1980), 81-93.
• [9] Guadalupe, I.V., Rodriguez, L., Normal Curvature of Surfaces in Space Forms, Pacific J. Math., 106(1983), 95-103.
• [10] Lumiste, U., Classification of Two-codimensional Semi-symmetric Submanifolds. TRU Toime- tised, 803(1988), 79-84.
• [11] Mihai, I. and Rouxel, B., Tensor product surfaces of Euclidean plane curves, Results in Mathematics, 27 (1995), no. 3-4, 308-315.
• [12] Mihai, I. and Rouxel, B., Tensor product surfaces of Euclidean Plane Curves, Geometry and Topology of Submanifolds, VII, World Scientific, (1994), 189-192.
• [13] Mihai, I., Rosca, R., Verstraelen, L., Vrancken, L., Tensor Product Surfaces of Euclidean Planar Curves, Rend. Sem. Mat. Messina, 3(1994/1995), 173-184.
• [14] Mihai, I., Van de Woestyne, I., Verstraelen, L. and Walrave, J., Tensor Product Surfaces of Lorentzian Planar Curves, Bull. Inst. Math. Acad. Sinica, 23(1995), no.4, 357-363.
• [15] Ozgur, C., Arslan, K., Murathan, C., On a Class of Surfaces in Euclidean Spaces, Commun. Fac. Sci. Univ. Ank. series A1, 51(2002), 47-54.
• [16] Szabo, Z.I., Structure Theorems on Riemannian Spaces Satisfying R(X,Y)·R=0. I. The local version, J. Differential Geometry, 17(1982), 531-582.