Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2011, Cilt: 4 Sayı: 2, 85 - 113, 30.10.2011

Roland Hildebrand

Öz

Kaynakça

  • [1] Alekseevsky, D.V., Medori, C. and Tomassini, A., Homogeneous para-Kähler Einstein mani- folds, Russ. Math. Surv., 64(2009), no. 1, 1–43.
  • [2] Amari, S., Differential-Geometrical Methods in Statistics, Vol. 28 of Lecture Notes in Statis- tics, Springer, 1990.
  • [3] Arhangelskii, A.V., ed., General Topology III, Springer, 1995.
  • [4] Chen, B.-Y., Lagrangian H-umbilical submanifolds of para-Kähler manifolds, Taiwanese J. Math., (to appear).
  • [5] Chen, B.-Y., Lagrangian submanifolds in para-Kähler manifolds, Nonlinear Analysis, 73(2010), no. 11, 3561–3571.
  • [6] Chen, B.-Y., Pseudo-Riemannan geometry, δ-invariants and applications, World Scientific, 2011.
  • [7] Chursin, M., Schäfer, L. and Smoczyk, K., Mean curvature flow of space-like Lagrangian submanifolds in almost para-Kähler manifolds, Calc. Var., 41(2010), no. 1–2, 111–125.
  • [8] Cortés, V., Mayer, C., Mohaupt, T. and Saueressig, F., Special geometry of Euclidean super- symmetry I: Vector multiplets, J. High Energy Phys., 03(2004), 028.
  • [9] Cortés, V., Lawn, M.A. and Schäfer, L., Affine hyperspheres associated to special para-Kähler manifolds, Int. J. Geom. Methods M., 3(2006), 995–1009.
  • [10] Cruceanu, V., Fortuny, P. and Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), no. 1, 83–115.
  • [11] Etayo, F., Santamaría, R. and Trías, U.R., The geometry of a bi-Lagrangian manifold, Differ. Geom. Appl., 24(2006), no. 1, 33–59.
  • [12] Gadea, P.M. and Montesinos Amilibia, A., The paracomplex projective spaces as symmetric and natural spaces, Indian J. Pure Appl. Math., 23(1992), no. 4, 261–275.
  • [13] Gelfand, I., Retakh, V. and Shubin, M., Fedosov manifolds, Adv. Math., 136(1998), 104–140.
  • [14] Libermann, P., Sur le problème d’équivalence de certaines structures infinit´esimales, Ann.Mat. Pura Appl., 36(1954), 27–120.
  • [15] Loftin, J.C., Affine spheres and Kähler-Einstein metrics, Math. Res. Lett., 9(2002), no. 4, 425–432.
  • [16] Munkres, J.R., Elementary differential topology, Vol. 54 of Ann. of Math. Stud., Princeton University Press, Princeton, NJ, 1966.
  • [17] Nomizu, K. and Sasaki, T., Affine differential geometry: geometry of affine immersions, Vol. 111 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1994.
  • [18] Raschewski, P.K., Riemannsche Geometrie und Tensoranalysis, Vol. 42 of Hochschulbücher für Mathematik, Deutscher Verlag der Wissenschaften, Berlin, 1959.
  • [19] Shima, H., Geometry of Hessian Structures, World Scientific, Hackensack, New Jersey, 2007.
  • [20] Weyl, H., Zur Infinitesimalgeometrie: Einordnung der projektiven und konformen Auffassung, G¨ottinger Nachr., 1921, 99–112.

HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS

Yıl 2011, Cilt: 4 Sayı: 2, 85 - 113, 30.10.2011

Roland Hildebrand

Öz


Anahtar Kelimeler

para-Kähler manifold Lagrangian immersion Codazzi structure affine differential geometry

Kaynakça

  • [1] Alekseevsky, D.V., Medori, C. and Tomassini, A., Homogeneous para-Kähler Einstein mani- folds, Russ. Math. Surv., 64(2009), no. 1, 1–43.
  • [2] Amari, S., Differential-Geometrical Methods in Statistics, Vol. 28 of Lecture Notes in Statis- tics, Springer, 1990.
  • [3] Arhangelskii, A.V., ed., General Topology III, Springer, 1995.
  • [4] Chen, B.-Y., Lagrangian H-umbilical submanifolds of para-Kähler manifolds, Taiwanese J. Math., (to appear).
  • [5] Chen, B.-Y., Lagrangian submanifolds in para-Kähler manifolds, Nonlinear Analysis, 73(2010), no. 11, 3561–3571.
  • [6] Chen, B.-Y., Pseudo-Riemannan geometry, δ-invariants and applications, World Scientific, 2011.
  • [7] Chursin, M., Schäfer, L. and Smoczyk, K., Mean curvature flow of space-like Lagrangian submanifolds in almost para-Kähler manifolds, Calc. Var., 41(2010), no. 1–2, 111–125.
  • [8] Cortés, V., Mayer, C., Mohaupt, T. and Saueressig, F., Special geometry of Euclidean super- symmetry I: Vector multiplets, J. High Energy Phys., 03(2004), 028.
  • [9] Cortés, V., Lawn, M.A. and Schäfer, L., Affine hyperspheres associated to special para-Kähler manifolds, Int. J. Geom. Methods M., 3(2006), 995–1009.
  • [10] Cruceanu, V., Fortuny, P. and Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), no. 1, 83–115.
  • [11] Etayo, F., Santamaría, R. and Trías, U.R., The geometry of a bi-Lagrangian manifold, Differ. Geom. Appl., 24(2006), no. 1, 33–59.
  • [12] Gadea, P.M. and Montesinos Amilibia, A., The paracomplex projective spaces as symmetric and natural spaces, Indian J. Pure Appl. Math., 23(1992), no. 4, 261–275.
  • [13] Gelfand, I., Retakh, V. and Shubin, M., Fedosov manifolds, Adv. Math., 136(1998), 104–140.
  • [14] Libermann, P., Sur le problème d’équivalence de certaines structures infinit´esimales, Ann.Mat. Pura Appl., 36(1954), 27–120.
  • [15] Loftin, J.C., Affine spheres and Kähler-Einstein metrics, Math. Res. Lett., 9(2002), no. 4, 425–432.
  • [16] Munkres, J.R., Elementary differential topology, Vol. 54 of Ann. of Math. Stud., Princeton University Press, Princeton, NJ, 1966.
  • [17] Nomizu, K. and Sasaki, T., Affine differential geometry: geometry of affine immersions, Vol. 111 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1994.
  • [18] Raschewski, P.K., Riemannsche Geometrie und Tensoranalysis, Vol. 42 of Hochschulbücher für Mathematik, Deutscher Verlag der Wissenschaften, Berlin, 1959.
  • [19] Shima, H., Geometry of Hessian Structures, World Scientific, Hackensack, New Jersey, 2007.
  • [20] Weyl, H., Zur Infinitesimalgeometrie: Einordnung der projektiven und konformen Auffassung, G¨ottinger Nachr., 1921, 99–112.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Roland Hildebrand Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 4 Sayı: 2

Kaynak Göster

APA Hildebrand, R. (2011). HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. International Electronic Journal of Geometry, 4(2), 85-113.
AMA Hildebrand R. HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. Int. Electron. J. Geom. Ekim 2011;4(2):85-113.
Chicago Hildebrand, Roland. “HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS”. International Electronic Journal of Geometry 4, sy. 2 (Ekim 2011): 85-113.
EndNote Hildebrand R (01 Ekim 2011) HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. International Electronic Journal of Geometry 4 2 85–113.
IEEE R. Hildebrand, “HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS”, Int. Electron. J. Geom., c. 4, sy. 2, ss. 85–113, 2011.
ISNAD Hildebrand, Roland. “HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS”. International Electronic Journal of Geometry 4/2 (Ekim 2011), 85-113.
JAMA Hildebrand R. HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. Int. Electron. J. Geom. 2011;4:85–113.
MLA Hildebrand, Roland. “HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS”. International Electronic Journal of Geometry, c. 4, sy. 2, 2011, ss. 85-113.
Vancouver Hildebrand R. HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. Int. Electron. J. Geom. 2011;4(2):85-113.