Research Article
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Year 2011, Volume 4, Issue 2, 85 - 113, 30.10.2011

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

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.

Details

Primary Language English
Journal Section Research Article
Authors

Roland HİLDEBRAND This is me

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

Cite

Bibtex @research article { iejg599493, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2011}, volume = {4}, number = {2}, pages = {85 - 113}, title = {HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS}, key = {cite}, author = {Hildebrand, Roland} }
APA Hildebrand, R. (2011). HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS . International Electronic Journal of Geometry , 4 (2) , 85-113 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/47488/599493
MLA Hildebrand, R. "HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS" . International Electronic Journal of Geometry 4 (2011 ): 85-113 <https://dergipark.org.tr/en/pub/iejg/issue/47488/599493>
Chicago Hildebrand, R. "HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS". International Electronic Journal of Geometry 4 (2011 ): 85-113
RIS TY - JOUR T1 - HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS AU - RolandHildebrand Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 85 EP - 113 VL - 4 IS - 2 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS %A Roland Hildebrand %T HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS %D 2011 %J International Electronic Journal of Geometry %P -1307-5624 %V 4 %N 2 %R %U
ISNAD Hildebrand, Roland . "HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS". International Electronic Journal of Geometry 4 / 2 (October 2011): 85-113 .
AMA Hildebrand R. HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. Int. Electron. J. Geom.. 2011; 4(2): 85-113.
Vancouver Hildebrand R. HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS. International Electronic Journal of Geometry. 2011; 4(2): 85-113.
IEEE R. Hildebrand , "HALF-DIMENSIONAL IMMERSIONS IN PARA-KÄHLER MANIFOLDS", International Electronic Journal of Geometry, vol. 4, no. 2, pp. 85-113, Oct. 2011