Araştırma Makalesi
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Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane

Yıl 2011, Cilt: 4 Sayı: 1, 1 - 14, 30.04.2011

Öz


Kaynakça

  • [1] Chen, B.-Y., Geometry of submanifolds and Its applications. Science University of Tokyo, Tokyo, 1981.
  • [2] Chen, B.-Y., Total mean curvature and submanifolds of finite type, World Scientific, New Jersey, 1984.
  • [3] Chen, B.-Y., Interaction of Legendre curves and Lagrangian submanifolds, Israel J. Math. 99 (1997), 69–108.
  • [4] Chen, B.-Y., Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tˆohoku Math. J., 49 (1997), no. 2, 277–297.
  • [5] Chen, B.-Y., Representation of flat Lagrangian H-umbilical submanifolds in complex Eu- clidean spaces, Tohoku Math. J., 51 (1999), no. 1, 13–20.
  • [6] Chen, B.-Y., Riemannian submanifolds, in: Handbook of Differential Geometry, Vol. I, 187– 418, North-Holland, Amsterdam, (eds. F. Dillen and L. Verstraelen), 2000.
  • [7] Chen, B.-Y., Riemannian geometry of Lagrangian submanifolds, Taiwanese J. Math., 5 (2001), no. 4, 681–723.
  • [8] Chen, B.-Y., Lagrangian submanifolds in para-K¨ahler manifolds, Nonlinear Analysis, 73 (2010), no. 11, 3561–3571.
  • [9] Chen, B.-Y., Lagrangian H-umbilical submanifolds of para-K¨ahler manifolds, Taiwanese J. Math., (to appear).
  • [10] Chen, B.-Y. and Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc., 193 (1974), 257–266.
  • [11] Cort´es, V., The special geometry of Euclidean supersymmetry: a survey, Rev. Un. Mat. Argentina, 47 (2006), no. 1, 29–34.
  • [12] Cort´es, V., Lawn, M.-A. and Sch¨afer, L., Affine hyperspheres associated to special para- K¨ahler manifolds, Int. J. Geom. Methods Mod. Phys., 3 (2006), no. 5–6, 995–1009.
  • [13] Cort´es, V., Mayer, C., Mohaupt, T. and Saueressig, F., Special geometry of Euclidean super- symmetry. I, Vector multiplets, J. High Energy Phys., 2004, no. 3, 028, 73 pp.
  • [14] Etayo, F., Santamar´ıa, R. and Tr´ıas, U. R., The geometry of a bi-Lagrangian manifold, Differential Geom. Appl., 24 (2006), no. 1, 33–59.
  • [15] Hou, Z., Deng, S. and Kaneyuki, S., Dipolarizations in compact Lie algebras and homogeneous para-Ka¨hler manifold, Tokyo J. Math., 20 (1997), no. 2, 381–388.
  • [16] Ponge, R. and Reckziegel, H., Twisted products in pseudo-Riemannian geometry, Geometriae Dedicata, 48 (1993), no. 1, 15–25.
  • [17] Rashevskij, P. K., The scalar field in a stratified space, Trudy Sem. Vektor. Tenzor. Anal., 6 (1948), 225–248.
  • [18] Rozenfeld, B. A., On unitary and stratified spaces, Trudy Sem. Vektor. Tenzor. Anal., 7 (1949), 260–275.
  • [19] Ruse, H. S., On parallel fields of planes in a Riemannian manifold, Quart. J. Math. Oxford Ser., 20 (1949), 218–234.
Yıl 2011, Cilt: 4 Sayı: 1, 1 - 14, 30.04.2011

Öz

Kaynakça

  • [1] Chen, B.-Y., Geometry of submanifolds and Its applications. Science University of Tokyo, Tokyo, 1981.
  • [2] Chen, B.-Y., Total mean curvature and submanifolds of finite type, World Scientific, New Jersey, 1984.
  • [3] Chen, B.-Y., Interaction of Legendre curves and Lagrangian submanifolds, Israel J. Math. 99 (1997), 69–108.
  • [4] Chen, B.-Y., Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tˆohoku Math. J., 49 (1997), no. 2, 277–297.
  • [5] Chen, B.-Y., Representation of flat Lagrangian H-umbilical submanifolds in complex Eu- clidean spaces, Tohoku Math. J., 51 (1999), no. 1, 13–20.
  • [6] Chen, B.-Y., Riemannian submanifolds, in: Handbook of Differential Geometry, Vol. I, 187– 418, North-Holland, Amsterdam, (eds. F. Dillen and L. Verstraelen), 2000.
  • [7] Chen, B.-Y., Riemannian geometry of Lagrangian submanifolds, Taiwanese J. Math., 5 (2001), no. 4, 681–723.
  • [8] Chen, B.-Y., Lagrangian submanifolds in para-K¨ahler manifolds, Nonlinear Analysis, 73 (2010), no. 11, 3561–3571.
  • [9] Chen, B.-Y., Lagrangian H-umbilical submanifolds of para-K¨ahler manifolds, Taiwanese J. Math., (to appear).
  • [10] Chen, B.-Y. and Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc., 193 (1974), 257–266.
  • [11] Cort´es, V., The special geometry of Euclidean supersymmetry: a survey, Rev. Un. Mat. Argentina, 47 (2006), no. 1, 29–34.
  • [12] Cort´es, V., Lawn, M.-A. and Sch¨afer, L., Affine hyperspheres associated to special para- K¨ahler manifolds, Int. J. Geom. Methods Mod. Phys., 3 (2006), no. 5–6, 995–1009.
  • [13] Cort´es, V., Mayer, C., Mohaupt, T. and Saueressig, F., Special geometry of Euclidean super- symmetry. I, Vector multiplets, J. High Energy Phys., 2004, no. 3, 028, 73 pp.
  • [14] Etayo, F., Santamar´ıa, R. and Tr´ıas, U. R., The geometry of a bi-Lagrangian manifold, Differential Geom. Appl., 24 (2006), no. 1, 33–59.
  • [15] Hou, Z., Deng, S. and Kaneyuki, S., Dipolarizations in compact Lie algebras and homogeneous para-Ka¨hler manifold, Tokyo J. Math., 20 (1997), no. 2, 381–388.
  • [16] Ponge, R. and Reckziegel, H., Twisted products in pseudo-Riemannian geometry, Geometriae Dedicata, 48 (1993), no. 1, 15–25.
  • [17] Rashevskij, P. K., The scalar field in a stratified space, Trudy Sem. Vektor. Tenzor. Anal., 6 (1948), 225–248.
  • [18] Rozenfeld, B. A., On unitary and stratified spaces, Trudy Sem. Vektor. Tenzor. Anal., 7 (1949), 260–275.
  • [19] Ruse, H. S., On parallel fields of planes in a Riemannian manifold, Quart. J. Math. Oxford Ser., 20 (1949), 218–234.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Bang-yen Chen

Yayımlanma Tarihi 30 Nisan 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 4 Sayı: 1

Kaynak Göster

APA Chen, B.-y. (2011). Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane. International Electronic Journal of Geometry, 4(1), 1-14.
AMA Chen By. Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane. Int. Electron. J. Geom. Nisan 2011;4(1):1-14.
Chicago Chen, Bang-yen. “Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler N-Plane”. International Electronic Journal of Geometry 4, sy. 1 (Nisan 2011): 1-14.
EndNote Chen B-y (01 Nisan 2011) Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane. International Electronic Journal of Geometry 4 1 1–14.
IEEE B.-y. Chen, “Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane”, Int. Electron. J. Geom., c. 4, sy. 1, ss. 1–14, 2011.
ISNAD Chen, Bang-yen. “Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler N-Plane”. International Electronic Journal of Geometry 4/1 (Nisan 2011), 1-14.
JAMA Chen B-y. Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane. Int. Electron. J. Geom. 2011;4:1–14.
MLA Chen, Bang-yen. “Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler N-Plane”. International Electronic Journal of Geometry, c. 4, sy. 1, 2011, ss. 1-14.
Vancouver Chen B-y. Classification of Flat Lagrangian H-Umbilical Submanifolds In Para-Kähler n-Plane. Int. Electron. J. Geom. 2011;4(1):1-14.