Research Article
BibTex RIS Cite

CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES

Year 2013, Volume: 6 Issue: 2, 1 - 8, 30.10.2013

Abstract


References

  • [1] Aiyama, R., Lagrangian surfaces in the complex 2-space, in: Proceedings of the Fifth Inter- national Workshop on Differential Geometry (Taegu, 2000), 25–29, Kyungpook Natl. Univ., Taegu, 2001.
  • [2] Aiyama, R., Lagrangian surfaces with circle symmetry in the complex 2-space, Michigan Math. J. 52(2004), no. 3, 491–506.
  • [3] Chen, B.-Y., Geometry of Submanifolds, M. Dekker, New York, 1973.
  • [4] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Arch.Math. 60(1993), no. 6, 568–578.
  • [5] Chen, B.-Y., Some new obstruction to minimal and Lagrangian isometric immersions, Japan. J. Math. 26(2000), no. 1, 105–127.
  • [6] Chen, B.-Y., Lagrangian surfaces of constant curvature in complex Euclidean plane, Tohoku Math J. 56(2004), no. 4, 289–298.
  • [7] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex Euclidean plane, Proc. Edinburgh Math. Soc. 48(2005), no. 2, 337–364.
  • [8] Chen, B.-Y., Maslovian Lagrangian surfaces of constant curvature in complex projective or complex hyperbolic planes, Math. Nachr. 278(2005), no. 11, 1242–1281.
  • [9] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex complex projective planes, J. Geom. Phys. 53(2005), no. 4, 428-460.
  • [10] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex hyperbolic planes, J. Geom. Phys. 55(2005), no. 4, 399-439.
  • [11] Chen, B.-Y., Three additional families of Lagrangian surfaces of constant curvature in com- plex projective plane, J. Geom. Phys. 56(2006), no. 4, 666–669.
  • [12] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex hyperbolic planes, II, Soochow J. Math. 33(2007), no. 1, 127–165.
  • [13] Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and Applications, World Scientific Publ., Hackensack, New Jersey, 2011.
  • [14] Chen, B.-Y. and Morvan, J.-M., Deformations of isotropic submanifolds in Kähler manifolds, J. Geom. Phys. 13(1994), no. 1, 79–104.
  • [15] Chen, B.-Y. and Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc. 193(1974), 257–266.
  • [16] Joyce, D., Special Lagrangian m-folds in Cm with symmetries, Duke Math. J. 115(2002), no. 1, 1–51.
  • [17] Reckziegel, H., Horizontal lifts of isometric immersions into the bundle space of a pseudo- Riemannian submersion, in: Global Differential Geometry and Global Analysis (1984). Lec- ture Notes in Math. 1156(1985), 264–279.
  • [18] Weinstein, A., Lectures on symplectic manifolds, Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976. Regional Conference Series in Mathematics, No. 29. American Mathematical Society, Providence, R.I.,1977.
Year 2013, Volume: 6 Issue: 2, 1 - 8, 30.10.2013

Abstract

References

  • [1] Aiyama, R., Lagrangian surfaces in the complex 2-space, in: Proceedings of the Fifth Inter- national Workshop on Differential Geometry (Taegu, 2000), 25–29, Kyungpook Natl. Univ., Taegu, 2001.
  • [2] Aiyama, R., Lagrangian surfaces with circle symmetry in the complex 2-space, Michigan Math. J. 52(2004), no. 3, 491–506.
  • [3] Chen, B.-Y., Geometry of Submanifolds, M. Dekker, New York, 1973.
  • [4] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Arch.Math. 60(1993), no. 6, 568–578.
  • [5] Chen, B.-Y., Some new obstruction to minimal and Lagrangian isometric immersions, Japan. J. Math. 26(2000), no. 1, 105–127.
  • [6] Chen, B.-Y., Lagrangian surfaces of constant curvature in complex Euclidean plane, Tohoku Math J. 56(2004), no. 4, 289–298.
  • [7] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex Euclidean plane, Proc. Edinburgh Math. Soc. 48(2005), no. 2, 337–364.
  • [8] Chen, B.-Y., Maslovian Lagrangian surfaces of constant curvature in complex projective or complex hyperbolic planes, Math. Nachr. 278(2005), no. 11, 1242–1281.
  • [9] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex complex projective planes, J. Geom. Phys. 53(2005), no. 4, 428-460.
  • [10] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex hyperbolic planes, J. Geom. Phys. 55(2005), no. 4, 399-439.
  • [11] Chen, B.-Y., Three additional families of Lagrangian surfaces of constant curvature in com- plex projective plane, J. Geom. Phys. 56(2006), no. 4, 666–669.
  • [12] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex hyperbolic planes, II, Soochow J. Math. 33(2007), no. 1, 127–165.
  • [13] Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and Applications, World Scientific Publ., Hackensack, New Jersey, 2011.
  • [14] Chen, B.-Y. and Morvan, J.-M., Deformations of isotropic submanifolds in Kähler manifolds, J. Geom. Phys. 13(1994), no. 1, 79–104.
  • [15] Chen, B.-Y. and Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc. 193(1974), 257–266.
  • [16] Joyce, D., Special Lagrangian m-folds in Cm with symmetries, Duke Math. J. 115(2002), no. 1, 1–51.
  • [17] Reckziegel, H., Horizontal lifts of isometric immersions into the bundle space of a pseudo- Riemannian submersion, in: Global Differential Geometry and Global Analysis (1984). Lec- ture Notes in Math. 1156(1985), 264–279.
  • [18] Weinstein, A., Lectures on symplectic manifolds, Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976. Regional Conference Series in Mathematics, No. 29. American Mathematical Society, Providence, R.I.,1977.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bang-yen Chen

Publication Date October 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

APA Chen, B.-y. (2013). CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES. International Electronic Journal of Geometry, 6(2), 1-8.
AMA Chen By. CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES. Int. Electron. J. Geom. October 2013;6(2):1-8.
Chicago Chen, Bang-yen. “CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES”. International Electronic Journal of Geometry 6, no. 2 (October 2013): 1-8.
EndNote Chen B-y (October 1, 2013) CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES. International Electronic Journal of Geometry 6 2 1–8.
IEEE B.-y. Chen, “CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES”, Int. Electron. J. Geom., vol. 6, no. 2, pp. 1–8, 2013.
ISNAD Chen, Bang-yen. “CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES”. International Electronic Journal of Geometry 6/2 (October 2013), 1-8.
JAMA Chen B-y. CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES. Int. Electron. J. Geom. 2013;6:1–8.
MLA Chen, Bang-yen. “CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES”. International Electronic Journal of Geometry, vol. 6, no. 2, 2013, pp. 1-8.
Vancouver Chen B-y. CLASSIFICATION OF SPHERICAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACES. Int. Electron. J. Geom. 2013;6(2):1-8.