Abstract
We give a characterization for an affine immersion from an almost product manifold the almost product structure of which is adjoint or skew-adjoint with respect to its affine fundamental form by the relative nullity distribution.
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Abe K.: On a class of hypersurface of \({\mathbb{R}^{n+1}}\). Duke Math. J. 41, 865–874 (1974)
Abe K., Magid M.: Relative nullity foliations and indefinite isometric immersions. Pacific J. Math. 124, 1–20 (1986)
Cortes V.: The special geometry of Euclidean supersymmetry. Rev. Un. Mat. Argentina 47, 29–34 (2006)
Cortes V., Lawn M.-A., Schäfer L.: Affine hyperspheres associated to special para-Kähler manifolds. Int. J. Geom. Methods Mod. Phys. 3, 995–1009 (2006)
Furuhata H.: A cylinder theorem for isometric pluriharmonic immersions. Geom. Dedicata. 66, 303–311 (1997)
Kurosu S.: A cylinder theorem for a (1, 1)-geodesic affine immersion. Int. J. Pura Appl. Math. 11, 181–204 (2004)
Kurosu S.: Relative nullity distributions and (1, 1)-geodesic affine immersions. Results Math. 56, 259–273 (2009)
Lawn M-A., Schäfer L.: Decompositions of para-complex vector bundles and para-complex affine immersions. Results Math. 48, 246–274 (2005)
Libermann P.: Sur le probleme d’equivalence de certains structures infinitesimales. Ann. Mat. Pura Appl. 36, 27–120 (1954)
Rozenfeld B.A.: On unitary and stratified spaces. Trudy Sem. Vektor. Tenzor. Anal. 7, 260–275 (1949)
Schäfer L.: tt*-bundles in para-complex geometry, special para-Kähler manifolds and para-pluriharmonic maps. Differential Geom. Appl. 24, 60–89 (2006)
Yano K., Kon M.: Structures on manifolds. World Scientific Publishing Co., Singapore (1984)
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Kurosu, S. Relative nullity distributions, an affine immersion from an almost product manifold and a para-pluriharmonic isometric immersion. Ann Glob Anal Geom 42, 333–347 (2012). https://doi.org/10.1007/s10455-012-9315-3
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DOI: https://doi.org/10.1007/s10455-012-9315-3
Keywords
- Cylinder theorem
- Relative nullity distribution
- Almost product manifold
- Para-complex manifold
- Para-pluriharmonic map