Research Article
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Year 2011, Volume 4, Issue 2, 32 - 62, 30.10.2011

Abstract

References

  • [1] Alekseevsky, D.V., Medori, C. and Tomassini, A., Homogeneous para-Kähler Einstein manifolds, Russ. Math. Surv., 64(2009), no. 1, 1–43.
  • [2] Ariyawansa, K.A., Davidon, W.C. and McKennon, K.D., A coordinate-free foundation for projective spaces treating projective maps from a subset of a vector space into another vector space, Tech. Rep. 2004-4, Washington State Univ., 2004.
  • [3] Calabi, E., Hypersurfaces with maximal affinely invariant area, Amer. J. Math., 104(1982), no. 1, 91-126.
  • [4] Chen, B.-Y., Lagrangian submanifolds in para-Kähler manifolds, Nonlinear Analysis, 73(2010), no. 11, 3561–3571.
  • [5] Chursin, M., Sch¨afer, L. and Smoczyk, K., Mean curvature flow of space-like Lagrangian submanifolds in almost para-K¨ahler manifolds, Calc. Var., 41(2010), no. 1–2, 111–125.
  • [6] 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.
  • [7] Cruceanu, V., Fortuny, P. and Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), no. 1, 83–115.
  • [8] Etayo, F., Santamaría, R. and Trías, U.R., The geometry of a bi-Lagrangian manifold, Differ. Geom. Appl., 24(2006), no. 1, 33–59.
  • [9] 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.
  • [10] Gadea, P.M. and Montesinos Amilibia, A., Spaces of constant para-holomorphic sectional curvature, Pac. J. Math., 136(1989), no. 1, 85–101.
  • [11] Hildebrand, R., Half-dimensional immersions in para-K¨ahler manifolds, Int. Electron. J. Geom., 4(2011), no.2, 85-113.
  • [12] Kobayashi, S. and Nomizu, K., Foundations of differential geometry II, Interscience publish- ers, New York, London, Sydney, 1969.
  • [13] Libermann, P., Sur le probl`eme d’équivalence de certaines structures infinit´esimales, Ann. Mat. Pura Appl., 36(1954), 27–120.
  • [14] Loftin, J.C., Affine spheres and Kähler-Einstein metrics, Math. Res. Lett., 9(2002), no. 4, 425–432.
  • [15] Nomizu, K. and Sasaki, T., Affine differential geometry: geometry of affine immersions, Vol. 111 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1994.
  • [16] Shima, H., Geometry of Hessian Structures, World Scientific, Hackensack, New Jersey, 2007.
  • [17] Simon, U., A survey on Codazzi tensors, In memoriam Ernst Mohr, Mathematiker und Opfer des Faschismus, Vol. 8 of Forum der Berliner Math. Gesellschaft, 97-106, Berliner Math. Gesellschaft, Berlin, 2009.
  • [18] Vaisman, I., Symplectic curvature tensors, Monatshefte fu¨r Mathematik, 100(1985), no. 4, 299-327.
  • [19] Vrancken, L., Centroaffine differential geometry and its relations to horizontal submanifolds, PDEs, submanifolds and affine differential geometry, Vol. 57 of Banach Center Publ., 21-28, Polish Acad. Sci., Warsaw, 2002.

THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY

Year 2011, Volume 4, Issue 2, 32 - 62, 30.10.2011

Abstract


References

  • [1] Alekseevsky, D.V., Medori, C. and Tomassini, A., Homogeneous para-Kähler Einstein manifolds, Russ. Math. Surv., 64(2009), no. 1, 1–43.
  • [2] Ariyawansa, K.A., Davidon, W.C. and McKennon, K.D., A coordinate-free foundation for projective spaces treating projective maps from a subset of a vector space into another vector space, Tech. Rep. 2004-4, Washington State Univ., 2004.
  • [3] Calabi, E., Hypersurfaces with maximal affinely invariant area, Amer. J. Math., 104(1982), no. 1, 91-126.
  • [4] Chen, B.-Y., Lagrangian submanifolds in para-Kähler manifolds, Nonlinear Analysis, 73(2010), no. 11, 3561–3571.
  • [5] Chursin, M., Sch¨afer, L. and Smoczyk, K., Mean curvature flow of space-like Lagrangian submanifolds in almost para-K¨ahler manifolds, Calc. Var., 41(2010), no. 1–2, 111–125.
  • [6] 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.
  • [7] Cruceanu, V., Fortuny, P. and Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), no. 1, 83–115.
  • [8] Etayo, F., Santamaría, R. and Trías, U.R., The geometry of a bi-Lagrangian manifold, Differ. Geom. Appl., 24(2006), no. 1, 33–59.
  • [9] 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.
  • [10] Gadea, P.M. and Montesinos Amilibia, A., Spaces of constant para-holomorphic sectional curvature, Pac. J. Math., 136(1989), no. 1, 85–101.
  • [11] Hildebrand, R., Half-dimensional immersions in para-K¨ahler manifolds, Int. Electron. J. Geom., 4(2011), no.2, 85-113.
  • [12] Kobayashi, S. and Nomizu, K., Foundations of differential geometry II, Interscience publish- ers, New York, London, Sydney, 1969.
  • [13] Libermann, P., Sur le probl`eme d’équivalence de certaines structures infinit´esimales, Ann. Mat. Pura Appl., 36(1954), 27–120.
  • [14] Loftin, J.C., Affine spheres and Kähler-Einstein metrics, Math. Res. Lett., 9(2002), no. 4, 425–432.
  • [15] Nomizu, K. and Sasaki, T., Affine differential geometry: geometry of affine immersions, Vol. 111 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1994.
  • [16] Shima, H., Geometry of Hessian Structures, World Scientific, Hackensack, New Jersey, 2007.
  • [17] Simon, U., A survey on Codazzi tensors, In memoriam Ernst Mohr, Mathematiker und Opfer des Faschismus, Vol. 8 of Forum der Berliner Math. Gesellschaft, 97-106, Berliner Math. Gesellschaft, Berlin, 2009.
  • [18] Vaisman, I., Symplectic curvature tensors, Monatshefte fu¨r Mathematik, 100(1985), no. 4, 299-327.
  • [19] Vrancken, L., Centroaffine differential geometry and its relations to horizontal submanifolds, PDEs, submanifolds and affine differential geometry, Vol. 57 of Banach Center Publ., 21-28, Polish Acad. Sci., Warsaw, 2002.

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 { iejg599488, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2011}, volume = {4}, number = {2}, pages = {32 - 62}, title = {THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY}, key = {cite}, author = {Hildebrand, Roland} }
APA Hildebrand, R. (2011). THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY . International Electronic Journal of Geometry , 4 (2) , 32-62 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/47488/599488
MLA Hildebrand, R. "THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY" . International Electronic Journal of Geometry 4 (2011 ): 32-62 <https://dergipark.org.tr/en/pub/iejg/issue/47488/599488>
Chicago Hildebrand, R. "THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY". International Electronic Journal of Geometry 4 (2011 ): 32-62
RIS TY - JOUR T1 - THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY AU - RolandHildebrand Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 32 EP - 62 VL - 4 IS - 2 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY %A Roland Hildebrand %T THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY %D 2011 %J International Electronic Journal of Geometry %P -1307-5624 %V 4 %N 2 %R %U
ISNAD Hildebrand, Roland . "THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY". International Electronic Journal of Geometry 4 / 2 (October 2011): 32-62 .
AMA Hildebrand R. THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. Int. Electron. J. Geom.. 2011; 4(2): 32-62.
Vancouver Hildebrand R. THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. International Electronic Journal of Geometry. 2011; 4(2): 32-62.
IEEE R. Hildebrand , "THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY", International Electronic Journal of Geometry, vol. 4, no. 2, pp. 32-62, Oct. 2011