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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2011 / Cilt: 60 - Sayı: 1

ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD

İsmail GÖK
Çetin CAMCI
Hilmi HACISALİHOGLU H.
Sayfa
49–58
Yayın Tarihi
2011-02-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Morever, we calculate the formulas of Gaussian and mean curvatures of a surface in R3 (−3) .

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study surface theory in 3-dimensional almost contact metric manifolds by using cross product defined by Camcı [6] .
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Morever, we calculate the formulas of Gaussian and mean curvatures of a surface in R3 (−3) .
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Sasakian manifold · contact manifold · surface theory

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) .

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Bu Makaleye Atıf Yap

GÖK, İ., CAMCI, Ç., H., 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, Cilt: 60 - Sayı: 1, 49–58. https://ajindex.com/articles/747437

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Kaynakça (9)

  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.