Research Article
BibTex RIS Cite
Year 2018, Volume: 47 Issue: 2, 251 - 260, 01.04.2018

Abstract

References

  • Bolton, J., Dillen, F., Dioos, B. and Vrancken, L. Almost complex surfaces in the nearly Kähler S3 x S3, Tôhoku Math. J., 67, 1 - 17, 2015.
  • Bolton, J., Vrancken, L. and Woodward, L. M. On almost complex curves in the nearly Kähler 6-sphere, Quart. J. Math. Oxford Ser., 45 (2), 407 - 427, 1994.
  • Bolton, J., Vrancken, L. and Woodward, L. M. Totally real minimal surfaces with noncircular ellipse of curvature in the nearly Kähler 6-sphere, J. London. Math. Soc., 56 (2), 625 - 644, 1997.
  • Butruille, J. Homogeneous nearly Kähler manifolds, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, IRMA Lect. Math. Theor. Phys., 16, 399 - 423, 2010.
  • Chen, B. Y. On slant surfaces, Taiwanese J. Math., 3, 163 - 179, 1999.
  • Chen, B. Y. On slant surfaces, Geometry of Slant Submanifolds. Leuven (1990), preprint.
  • Dillen, F., Verstraelen, L. and Vrancken, L. Almost complex submanifolds of a 6-dimensional sphere II, Kodai Math. J., 10, 161 - 171, 1987.
  • Dillen, F., Verstraelen, L. and Vrancken, L. Classification of totally real 3-dimensional submanifolds of S6(1) with K  1=16, J. Math. Soc. Japan, 42, 565 - 584, 1990.
  • Dioos,B., Li, H., Ma, H. and Vrancken, L. Flat almost complex surfaces in the homogeneous nearly Kähler S3  S3, Results Math. 73:38, 2018.
  • Dioos, B., Vrancken, L. and Wang, X. Lagrangian submanifolds in the homogeneous nearly Kähler S3  S3, Ann. Glob. Anal. Geom. 53 (1), 39 - 66, 2018.
  • Hashimoto, H. and Mashimo, K. On some 3-dimensional CR submanifolds in S6, Nagoya Math. J., 156, 171 - 185, 1999.
  • Ejiri, N. Totally real submanifolds in a 6-sphere, Proc. Am. Math. Soc., 83, 759 - 763, 1981.
  • Li, X. A classification theorem for complete minimal surfaces in S6 with constant Kähler angles, Arch. Math., 72, 385 - 400, 1999.
  • Obrenovic, K. and Vukmirovic, S. Two classes of slant surfaces in the nearly Kähler six sphere, Rev. Unión Mat. Argent., 54, 111 - 121, 2013.
  • Podestà, F. and Spiro, A. 6-dimensional nearly Kähler manifolds of cohomogeneity one, J. Geom. Phys., 60, 156 - 164, 2010.
  • Shastri, A. R. Elements of differential topology, CRC press, Boca Raton (2011).

A class of slant surfaces of the nearly Kahler $S^3\times S^3$

Year 2018, Volume: 47 Issue: 2, 251 - 260, 01.04.2018

Abstract

We investigate slant surfaces of the nearly Kähler $S^3\times S^3$ which are
orbits of isometric actions, classify them and show that for a prescribed
angle there exists corresponding slant surface. Also, amongst them, we
find the totally geodesic ones.

References

  • Bolton, J., Dillen, F., Dioos, B. and Vrancken, L. Almost complex surfaces in the nearly Kähler S3 x S3, Tôhoku Math. J., 67, 1 - 17, 2015.
  • Bolton, J., Vrancken, L. and Woodward, L. M. On almost complex curves in the nearly Kähler 6-sphere, Quart. J. Math. Oxford Ser., 45 (2), 407 - 427, 1994.
  • Bolton, J., Vrancken, L. and Woodward, L. M. Totally real minimal surfaces with noncircular ellipse of curvature in the nearly Kähler 6-sphere, J. London. Math. Soc., 56 (2), 625 - 644, 1997.
  • Butruille, J. Homogeneous nearly Kähler manifolds, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, IRMA Lect. Math. Theor. Phys., 16, 399 - 423, 2010.
  • Chen, B. Y. On slant surfaces, Taiwanese J. Math., 3, 163 - 179, 1999.
  • Chen, B. Y. On slant surfaces, Geometry of Slant Submanifolds. Leuven (1990), preprint.
  • Dillen, F., Verstraelen, L. and Vrancken, L. Almost complex submanifolds of a 6-dimensional sphere II, Kodai Math. J., 10, 161 - 171, 1987.
  • Dillen, F., Verstraelen, L. and Vrancken, L. Classification of totally real 3-dimensional submanifolds of S6(1) with K  1=16, J. Math. Soc. Japan, 42, 565 - 584, 1990.
  • Dioos,B., Li, H., Ma, H. and Vrancken, L. Flat almost complex surfaces in the homogeneous nearly Kähler S3  S3, Results Math. 73:38, 2018.
  • Dioos, B., Vrancken, L. and Wang, X. Lagrangian submanifolds in the homogeneous nearly Kähler S3  S3, Ann. Glob. Anal. Geom. 53 (1), 39 - 66, 2018.
  • Hashimoto, H. and Mashimo, K. On some 3-dimensional CR submanifolds in S6, Nagoya Math. J., 156, 171 - 185, 1999.
  • Ejiri, N. Totally real submanifolds in a 6-sphere, Proc. Am. Math. Soc., 83, 759 - 763, 1981.
  • Li, X. A classification theorem for complete minimal surfaces in S6 with constant Kähler angles, Arch. Math., 72, 385 - 400, 1999.
  • Obrenovic, K. and Vukmirovic, S. Two classes of slant surfaces in the nearly Kähler six sphere, Rev. Unión Mat. Argent., 54, 111 - 121, 2013.
  • Podestà, F. and Spiro, A. 6-dimensional nearly Kähler manifolds of cohomogeneity one, J. Geom. Phys., 60, 156 - 164, 2010.
  • Shastri, A. R. Elements of differential topology, CRC press, Boca Raton (2011).
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Miroslava Antić This is me

Publication Date April 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 2

Cite

APA Antić, M. (2018). A class of slant surfaces of the nearly Kahler $S^3\times S^3$. Hacettepe Journal of Mathematics and Statistics, 47(2), 251-260.
AMA Antić M. A class of slant surfaces of the nearly Kahler $S^3\times S^3$. Hacettepe Journal of Mathematics and Statistics. April 2018;47(2):251-260.
Chicago Antić, Miroslava. “A Class of Slant Surfaces of the Nearly Kahler $S^3\times S^3$”. Hacettepe Journal of Mathematics and Statistics 47, no. 2 (April 2018): 251-60.
EndNote Antić M (April 1, 2018) A class of slant surfaces of the nearly Kahler $S^3\times S^3$. Hacettepe Journal of Mathematics and Statistics 47 2 251–260.
IEEE M. Antić, “A class of slant surfaces of the nearly Kahler $S^3\times S^3$”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, pp. 251–260, 2018.
ISNAD Antić, Miroslava. “A Class of Slant Surfaces of the Nearly Kahler $S^3\times S^3$”. Hacettepe Journal of Mathematics and Statistics 47/2 (April 2018), 251-260.
JAMA Antić M. A class of slant surfaces of the nearly Kahler $S^3\times S^3$. Hacettepe Journal of Mathematics and Statistics. 2018;47:251–260.
MLA Antić, Miroslava. “A Class of Slant Surfaces of the Nearly Kahler $S^3\times S^3$”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, 2018, pp. 251-60.
Vancouver Antić M. A class of slant surfaces of the nearly Kahler $S^3\times S^3$. Hacettepe Journal of Mathematics and Statistics. 2018;47(2):251-60.