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

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

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.

___

  • 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).