K. Arslan, B. Bulca, B. Kılıc, Y. H. Kim , C. Murathan and G. Ozturk, Tensor Product Surfaces with Pointwise 1-Type Gauss Map, Bull. Korean Math.Soc. 48 (2011), 601-609.
K. Arslan and C. Murathan, Tensor product surfaces of pseudo-Euclidean planar curves, Geometry and topology of submanifolds, VII (Leuven, 1994/Brussels, 1994) World Sci. Publ., River Edge, NJ (1995), 71-74.
B. Bulca and K. Arslan, Semiparallel tensor product surfaces in E4, Int. Electron. J. Geom., ,1,(2014), 36-43.
M. do Carmo, Riemannian geometry, Birkhauser, 1993.
B. Y. Chen, Geometry of Submanifolds, M. Dekker, New York 1973.
B. Y. Chen, Diğerential Geometry of semiring of immersions, I: General Theory Bull. Inst. Math. Acad. Sinica 21 (1993), 1-34.
F. Decruyenaere, F. Dillen, I. Mihai and L. Verstraelen, Tensor products of spherical and equivariant immersions Bull. Belg. Math. Soc.- Simon Stevin 1 (1994), 643-648.
F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken, The semiring of immersions of manifolds, Beitrage Algebra Geom. 34 (1993), 209-215.
J. Deprez, Semi- parallel Surfaces in Euclidean Space, J. Geom., 25 (1985), 192-200.
K. ·Ilarslan and E. Nesovic, Tensor product surfaces of a Lorentzian space curve and a Lorentzian plane curve, Bull. Inst. Math. Acad. Sinica 33 (2005), 151-171.
K. ·Ilarslan and E. Nesovic, Tensor product surfaces of a Euclidean space curve and a Lorentzian plane curve, Diğerential Geometry - Dynamical Systems 9 (2007),47-57.
I. Mihai, and B. Rouxel, Tensor Product Surfaces of Euclidean Plane Curves, Results in Mathematics, 27 (1995), no.3-4, 308-315.
I. Mihai, I. Van de Woestyne, L. Verstraelen and J. Walrave, Tensor product surfaces of a Lorentzian plane curve and a Euclidean plane curve. Rend. Sem. Mat. Messina Ser. II 3(18) (1994/95), 147–158.
B. O‘Neill, Semi - Riemannian Geometry, with applications to relavity, Academic Press. New York, (1983)
S. Özkaldı Karaku¸s and Y. Yayli, Bicomplex number and tensor product surfaces in R4, Ukrainian Math. J. 64 (2012), no. 3, 344–355.
S. Özkaldi and Y. Yayli, Tensor product surfaces in R4and Lie groups, Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 1, 69–77.
Z. I., Szabo, Structure theorems on Riemannian spaces satisfying R(X; Y )R = 0, I. The local version, J. Diğerential Geometry, 17 (1982), 531-582.
Current address : M. Yıldırım: Kırıkkale University, Faculty of Sciences and Arts, Department of Mathematics, 71450 Kırıkkale/ Turkey
E-mail address : myildirim@kku.edu.tr Current address : K. ·Ilarslan: Kırıkkale University, Faculty of Sciences and Arts, Department of Mathematics, 71450 Kırıkkale/ Turkey
E-mail address : kilarslan@kku.edu.tr
Year 2016,
Volume: 65 Issue: 2, 133 - 142, 01.08.2016
K. Arslan, B. Bulca, B. Kılıc, Y. H. Kim , C. Murathan and G. Ozturk, Tensor Product Surfaces with Pointwise 1-Type Gauss Map, Bull. Korean Math.Soc. 48 (2011), 601-609.
K. Arslan and C. Murathan, Tensor product surfaces of pseudo-Euclidean planar curves, Geometry and topology of submanifolds, VII (Leuven, 1994/Brussels, 1994) World Sci. Publ., River Edge, NJ (1995), 71-74.
B. Bulca and K. Arslan, Semiparallel tensor product surfaces in E4, Int. Electron. J. Geom., ,1,(2014), 36-43.
M. do Carmo, Riemannian geometry, Birkhauser, 1993.
B. Y. Chen, Geometry of Submanifolds, M. Dekker, New York 1973.
B. Y. Chen, Diğerential Geometry of semiring of immersions, I: General Theory Bull. Inst. Math. Acad. Sinica 21 (1993), 1-34.
F. Decruyenaere, F. Dillen, I. Mihai and L. Verstraelen, Tensor products of spherical and equivariant immersions Bull. Belg. Math. Soc.- Simon Stevin 1 (1994), 643-648.
F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken, The semiring of immersions of manifolds, Beitrage Algebra Geom. 34 (1993), 209-215.
J. Deprez, Semi- parallel Surfaces in Euclidean Space, J. Geom., 25 (1985), 192-200.
K. ·Ilarslan and E. Nesovic, Tensor product surfaces of a Lorentzian space curve and a Lorentzian plane curve, Bull. Inst. Math. Acad. Sinica 33 (2005), 151-171.
K. ·Ilarslan and E. Nesovic, Tensor product surfaces of a Euclidean space curve and a Lorentzian plane curve, Diğerential Geometry - Dynamical Systems 9 (2007),47-57.
I. Mihai, and B. Rouxel, Tensor Product Surfaces of Euclidean Plane Curves, Results in Mathematics, 27 (1995), no.3-4, 308-315.
I. Mihai, I. Van de Woestyne, L. Verstraelen and J. Walrave, Tensor product surfaces of a Lorentzian plane curve and a Euclidean plane curve. Rend. Sem. Mat. Messina Ser. II 3(18) (1994/95), 147–158.
B. O‘Neill, Semi - Riemannian Geometry, with applications to relavity, Academic Press. New York, (1983)
S. Özkaldı Karaku¸s and Y. Yayli, Bicomplex number and tensor product surfaces in R4, Ukrainian Math. J. 64 (2012), no. 3, 344–355.
S. Özkaldi and Y. Yayli, Tensor product surfaces in R4and Lie groups, Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 1, 69–77.
Z. I., Szabo, Structure theorems on Riemannian spaces satisfying R(X; Y )R = 0, I. The local version, J. Diğerential Geometry, 17 (1982), 531-582.
Current address : M. Yıldırım: Kırıkkale University, Faculty of Sciences and Arts, Department of Mathematics, 71450 Kırıkkale/ Turkey
E-mail address : myildirim@kku.edu.tr Current address : K. ·Ilarslan: Kırıkkale University, Faculty of Sciences and Arts, Department of Mathematics, 71450 Kırıkkale/ Turkey
Yıldırım, M., & Ilarslan, K. (2016). SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 133-142. https://doi.org/10.1501/Commua1_0000000765
AMA
Yıldırım M, Ilarslan K. SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2016;65(2):133-142. doi:10.1501/Commua1_0000000765
Chicago
Yıldırım, Mehmet, and Kazım Ilarslan. “SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 2 (August 2016): 133-42. https://doi.org/10.1501/Commua1_0000000765.
EndNote
Yıldırım M, Ilarslan K (August 1, 2016) SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 133–142.
IEEE
M. Yıldırım and K. Ilarslan, “SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 2, pp. 133–142, 2016, doi: 10.1501/Commua1_0000000765.
ISNAD
Yıldırım, Mehmet - Ilarslan, Kazım. “SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (August 2016), 133-142. https://doi.org/10.1501/Commua1_0000000765.
JAMA
Yıldırım M, Ilarslan K. SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:133–142.
MLA
Yıldırım, Mehmet and Kazım Ilarslan. “SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 2, 2016, pp. 133-42, doi:10.1501/Commua1_0000000765.
Vancouver
Yıldırım M, Ilarslan K. SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACEE4. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):133-42.