[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.
[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.
[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.
[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
[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.
[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.
[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.
[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.
Hildebrand, R. (2011). THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. International Electronic Journal of Geometry, 4(2), 32-62.
AMA
Hildebrand R. THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. Int. Electron. J. Geom. October 2011;4(2):32-62.
Chicago
Hildebrand, Roland. “THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY”. International Electronic Journal of Geometry 4, no. 2 (October 2011): 32-62.
EndNote
Hildebrand R (October 1, 2011) THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. International Electronic Journal of Geometry 4 2 32–62.
IEEE
R. Hildebrand, “THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY”, Int. Electron. J. Geom., vol. 4, no. 2, pp. 32–62, 2011.
ISNAD
Hildebrand, Roland. “THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY”. International Electronic Journal of Geometry 4/2 (October 2011), 32-62.
JAMA
Hildebrand R. THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. Int. Electron. J. Geom. 2011;4:32–62.
MLA
Hildebrand, Roland. “THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY”. International Electronic Journal of Geometry, vol. 4, no. 2, 2011, pp. 32-62.
Vancouver
Hildebrand R. THE CROSS-RATIO MANIFOLD: A MODEL OF CENTRO-AFFINE GEOMETRY. Int. Electron. J. Geom. 2011;4(2):32-6.