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Year 2011, Volume: 4 Issue: 2, 85 - 113, 30.10.2011

Roland Hildebrand

Abstract

References

  • [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

Year 2011, Volume: 4 Issue: 2, 85 - 113, 30.10.2011

Roland Hildebrand

Abstract


Keywords

para-Kähler manifold Lagrangian immersion Codazzi structure affine differential geometry

References

  • [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.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Roland Hildebrand This is me

Publication Date October 30, 2011
Published in Issue Year 2011 Volume: 4 Issue: 2

Cite

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. October 2011;4(2):85-113.
Chicago Hildebrand, Roland. “HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS”. International Electronic Journal of Geometry 4, no. 2 (October 2011): 85-113.
EndNote Hildebrand R (October 1, 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., vol. 4, no. 2, pp. 85–113, 2011.
ISNAD Hildebrand, Roland. “HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS”. International Electronic Journal of Geometry 4/2 (October 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, vol. 4, no. 2, 2011, pp. 85-113.
Vancouver Hildebrand R. HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. Int. Electron. J. Geom. 2011;4(2):85-113.