An Algebraic Characterization of Affine Manifolds with G-Structure Satisfying a Homogeneity Condition

Una caracterización algebraica de las variedades afines con G-estructura que satisfacen una condición de homogeneidad

We give an algebraic characterization of the possible characteristic tensors of an infinitesimally homogeneous affine manifold with G-structure. Such concepts were introduced in [6].

Presentamos una caracterización algebraica de los posibles tensores característicos de una variedad infinitesimalmente homogénea con G-estructura. Tales conceptos son introducidos en [6].

An Algebraic Characterization of Affine Manifolds with G-Structure Satisfying a Homogeneity Condition Una caracterización algebraica de las variedades afines con G-estructura que satisfacen una condición de homogeneidad CARLOS ALBERTO MARÍN1

1Universidad de Antioquia, Medellín, Colombia. Email:camara@matematicas.udea.edu.co 

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Abstract

We give an algebraic characterization of the possible characteristic tensors of an infinitesimally homogeneous affine manifold with G-structure. Such concepts were introduced in [6].

Key words: Infinitesimally homogeneous manifold, Inner torsion, G-structures.

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2000 Mathematics Subject Classification: 53A15, 53B05, 53C10, 53C30.

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Resumen

Palabras clave: Variedad infinitesimalmente homogénea, torsión interna, G-estructuras.

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Texto completo disponible en PDF

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References

[1] M. Dajczer, Submanifolds and Isometric Immersions, Publish or Perish, Houston, United States, 1990.

[2] B. Daniel, `Isometric Immersions into 3-Dimensional Homogeneous Manifolds´, Comment. Math. Helv. 82, 1 (2007), 87-131.

[3] B. Daniel, `Isometric Immersions into Sn\timesR and Hn\timesR and Applications to Minimal Surfaces´, Trans. Am. Math. Soc. 361, 12 (2009), 6255-6282.

[4] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic press, New York, United States, 1978.

[5] P. Piccione and D. Tausk, The Theory of Connections and G-Structures: Applications to Affine and Isometric Immersions, IMPA, Rio de Janeiro, Brazil, 2006.

[6] P. Piccione and D. Tausk, `An Existence Theorem for G-Structure Preserving Affine Immersions´, Indiana Univ. Math. J 57, 3 (2008), 1431-1465.

(Recibido en septiembre de 2010. Aceptado en octubre de 2010)

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv44n2a07, 
    AUTHOR  = {Marín, Carlos Alberto}, 
    TITLE   = {{An Algebraic Characterization of Affine Manifolds with \boldsymbol{G}-Structure Satisfying a Homogeneity Condition}}, 
    JOURNAL = {Revista Colombiana de Matemáticas}, 
    YEAR    = {2010}, 
    volume  = {44}, 
    number  = {2}, 
    pages   = {149-165} 
}