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

Year 2011, Volume: 60 Issue: 1, 49 - 58, 01.02.2011

İsmail Gök Çetin Camcı Hilmi Hacısalihoglu H.

https://doi.org/10.1501/Commua1_0000000668

Abstract

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) .

Keywords

Sasakian manifold, contact manifold, surface theory

References

[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.

Year 2011, Volume: 60 Issue: 1, 49 - 58, 01.02.2011

İsmail Gök Çetin Camcı Hilmi Hacısalihoglu H.

https://doi.org/10.1501/Commua1_0000000668

Abstract

References

[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.

There are 9 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	İsmail Gök This is me Çetin Camcı This is me Hilmi Hacısalihoglu H. This is me
Publication Date	February 1, 2011
Published in Issue	Year 2011 Volume: 60 Issue: 1

Cite

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. February 2011;60(1):49-58. doi:10.1501/Commua1_0000000668
Chicago	Gök, İsmail, Çetin Camcı, and 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, no. 1 (February 2011): 49-58. https://doi.org/10.1501/Commua1_0000000668.
EndNote	Gök İ, Camcı Ç, Hacısalihoglu H. H (February 1, 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, and H. Hacısalihoglu H., “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 60, no. 1, pp. 49–58, 2011, doi: 10.1501/Commua1_0000000668.
ISNAD	Gök, İsmail et al. “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60/1 (February 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 et al. “ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 60, no. 1, 2011, pp. 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.