ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD

İsmail Gök; Çetin Camcı; Hilmi Hacısalihoglu H.

doi:10.1501/Commua1_0000000668

ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD

Yıl 2011, Cilt: 60 Sayı: 1, 49 - 58, 01.02.2011

İsmail Gök Çetin Camcı Hilmi Hacısalihoglu H.

https://doi.org/10.1501/Commua1_0000000668

Öz

In this paper, we study surface theory in 3-dimensional almost
contact metric manifolds by using cross product defined by Camcı [6] . Camcı
also studied the theory of curves using the new cross product on this manifolds.
In this study, we have defined unit normal vector field of any surface in R3 (−3)
and then, we investigate shape operator matrix of the surface. Morever, we
calculate the formulas of Gaussian and mean curvatures of a surface in R3 (−3) .

Anahtar Kelimeler

Sasakian manifold, contact manifold, surface theory

Kaynakça

[1] B. Y. Chen, J. Dillen, F. Verstraelen and L. Vrancken, Curves of finite type, Geometry and topology of submanifolds, II (Avignon, 1998), 76-110, World Sci. Publ., Teaneck, NJ, 1990.
[2] C. Baikoussis and D. E. Blair, Finite type integral submanifold of the contact manifold , Bull. Math. Acad. Sinica , 19, (1991), 327-350.
[3] C. Baikoussis and D. E. Blair, On Legendre curves in contact 3-manifolds, Geom. Dedicata, 49, (1994), 135-142.
[4] C. Camci, A curves theory in contact geometry, Phd.thesis , (2007).
[5] C. Camci and H.H. Hacisalihoglu, Finite type curve in 3-dimensional Sasakian Manifold, Bulletin of the Korean Mathematical Society, 47, (2010), 1163-1170.
[6] C. Camci, Extended cross product in a 3−dimensional almost contact metric manifold with applications to curve theory, Turk. J. Math., 35, (2011), 1-14.
[7] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer, Berlin, Hiedelberg, New York, 1976.
[8] I. Gök, ˙ Surfaces Theory in contact geometry, Phd.thesis , (2010).
[9] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385.

Yıl 2011, Cilt: 60 Sayı: 1, 49 - 58, 01.02.2011

İsmail Gök Çetin Camcı Hilmi Hacısalihoglu H.

https://doi.org/10.1501/Commua1_0000000668

Öz

Kaynakça

[1] B. Y. Chen, J. Dillen, F. Verstraelen and L. Vrancken, Curves of finite type, Geometry and topology of submanifolds, II (Avignon, 1998), 76-110, World Sci. Publ., Teaneck, NJ, 1990.
[2] C. Baikoussis and D. E. Blair, Finite type integral submanifold of the contact manifold , Bull. Math. Acad. Sinica , 19, (1991), 327-350.
[3] C. Baikoussis and D. E. Blair, On Legendre curves in contact 3-manifolds, Geom. Dedicata, 49, (1994), 135-142.
[4] C. Camci, A curves theory in contact geometry, Phd.thesis , (2007).
[5] C. Camci and H.H. Hacisalihoglu, Finite type curve in 3-dimensional Sasakian Manifold, Bulletin of the Korean Mathematical Society, 47, (2010), 1163-1170.
[6] C. Camci, Extended cross product in a 3−dimensional almost contact metric manifold with applications to curve theory, Turk. J. Math., 35, (2011), 1-14.
[7] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer, Berlin, Hiedelberg, New York, 1976.
[8] I. Gök, ˙ Surfaces Theory in contact geometry, Phd.thesis , (2010).
[9] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385.

Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Research Article
Yazarlar	İsmail Gök Bu kişi benim Çetin Camcı Bu kişi benim Hilmi Hacısalihoglu H. Bu kişi benim
Yayımlanma Tarihi	1 Şubat 2011
Yayımlandığı Sayı	Yıl 2011 Cilt: 60 Sayı: 1

Kaynak Göster

APA	Gök, İ., Camcı, Ç., & Hacısalihoglu H., H. (2011). ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 60(1), 49-58. https://doi.org/10.1501/Commua1_0000000668
AMA	Gök İ, Camcı Ç, Hacısalihoglu H. H. ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2011;60(1):49-58. doi:10.1501/Commua1_0000000668
Chicago	Gök, İsmail, Çetin Camcı, ve Hilmi Hacısalihoglu H. “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60, sy. 1 (Şubat 2011): 49-58. https://doi.org/10.1501/Commua1_0000000668.
EndNote	Gök İ, Camcı Ç, Hacısalihoglu H. H (01 Şubat 2011) ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60 1 49–58.
IEEE	İ. Gök, Ç. Camcı, ve H. Hacısalihoglu H., “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 60, sy. 1, ss. 49–58, 2011, doi: 10.1501/Commua1_0000000668.
ISNAD	Gök, İsmail vd. “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60/1 (Şubat 2011), 49-58. https://doi.org/10.1501/Commua1_0000000668.
JAMA	Gök İ, Camcı Ç, Hacısalihoglu H. H. ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2011;60:49–58.
MLA	Gök, İsmail vd. “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 60, sy. 1, 2011, ss. 49-58, doi:10.1501/Commua1_0000000668.
Vancouver	Gök İ, Camcı Ç, Hacısalihoglu H. H. ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2011;60(1):49-58.