BibTex RIS Kaynak Göster

On the prolongations of homogeneous vector bundles

Yıl 2016, Cilt: 65 Sayı: 2, 47 - 54, 01.08.2016
https://doi.org/10.1501/Commua1_0000000758

Öz

In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation.For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous structure and its corresponding representationare derived. The prolongation of induced representation, which is an in finite dimensional linear representation, is also defined

Kaynakça

  • Adams, J. F., Lectures on Lie Groups , (Benjamin Inc., New York, 1969).
  • Boralevi, Ada., Sections of homogeneous vector bund les , Journal of Algebra 323, 2301-2317, (2010).
  • Bott, Raoul., Homogeneous Vector Bund les , Annals of mathematics, Vol. 66, No. 2, (1957).
  • Cordero, L. A., Dodson, C.T.J., De Leon, M., Diğerential Geometry of Frame Bundles, Kluwer Academic Press, (1989).
  • Brockett, R.W., Sussmann, H. J., Tangent Bundles of Homogeneous Spaces are Homogeneous Spaces , Proceedings of the American Mathematical Society, 35, 550-551 (1972).
  • Fisher, Robert and Laquer, H. Turner, Second order tangent vectors in Riemannian geometry. J. Korean Math. Soc.,36(5):959-1008, (1999).
  • Gri¢ ths, Philip A., On the Diğ erential Geometry of Homogeneous Bundles , (1963).
  • Haboush, W. J., Homogeneous Vector Bund les and Reductive Subgroups of Reductive Alge- braic Groups ,American Journal of Mathematics, Vol. 100, No. 6 , pp. 1123-1137 (1978).
  • Kadioglu, H., Esin, E., On the Prolongations of Representations of Lie Groups , Hadronic J. ,183-196, (2010).
  • Kadioglu, H., Esin, E.,Yaylı, Y. Prolongations of Lie Algebra Representations , Advances and Applications in Math. Sci. 10, no. 5, 533-542.(2011).
  • Kobayashi, S. Homogeneous Vector Bundles and Stability , Nagoya Math. J. Vol. 101, 37- ,(1986).
  • Kobayashi, S., Nomizu, K., Foundations of Diğ erential Geometry 1 , (Interscience Publishers, New York, 1963).
  • Purohit, G. N., Vector Bund les and Induced Representations of Lie Groups , Ganita Sandesh, , 17-20(1988).
  • Saunders D.J., The Geometry of Jet Bundles , (Cambridge University Press, Cambridge- New York, 1989).
  • Yano, K, Ishihara, S., Tangent and Cotangent Bundles , (M. Dekker, New York, 1973).
  • Current address : Hülya KADIO ¼GLU :Department of Mathematics Education, Yildiz Technical University Istanbul TURKEY E-mail address : hkadio@yildiz.edu.tr
Yıl 2016, Cilt: 65 Sayı: 2, 47 - 54, 01.08.2016
https://doi.org/10.1501/Commua1_0000000758

Öz

Kaynakça

  • Adams, J. F., Lectures on Lie Groups , (Benjamin Inc., New York, 1969).
  • Boralevi, Ada., Sections of homogeneous vector bund les , Journal of Algebra 323, 2301-2317, (2010).
  • Bott, Raoul., Homogeneous Vector Bund les , Annals of mathematics, Vol. 66, No. 2, (1957).
  • Cordero, L. A., Dodson, C.T.J., De Leon, M., Diğerential Geometry of Frame Bundles, Kluwer Academic Press, (1989).
  • Brockett, R.W., Sussmann, H. J., Tangent Bundles of Homogeneous Spaces are Homogeneous Spaces , Proceedings of the American Mathematical Society, 35, 550-551 (1972).
  • Fisher, Robert and Laquer, H. Turner, Second order tangent vectors in Riemannian geometry. J. Korean Math. Soc.,36(5):959-1008, (1999).
  • Gri¢ ths, Philip A., On the Diğ erential Geometry of Homogeneous Bundles , (1963).
  • Haboush, W. J., Homogeneous Vector Bund les and Reductive Subgroups of Reductive Alge- braic Groups ,American Journal of Mathematics, Vol. 100, No. 6 , pp. 1123-1137 (1978).
  • Kadioglu, H., Esin, E., On the Prolongations of Representations of Lie Groups , Hadronic J. ,183-196, (2010).
  • Kadioglu, H., Esin, E.,Yaylı, Y. Prolongations of Lie Algebra Representations , Advances and Applications in Math. Sci. 10, no. 5, 533-542.(2011).
  • Kobayashi, S. Homogeneous Vector Bundles and Stability , Nagoya Math. J. Vol. 101, 37- ,(1986).
  • Kobayashi, S., Nomizu, K., Foundations of Diğ erential Geometry 1 , (Interscience Publishers, New York, 1963).
  • Purohit, G. N., Vector Bund les and Induced Representations of Lie Groups , Ganita Sandesh, , 17-20(1988).
  • Saunders D.J., The Geometry of Jet Bundles , (Cambridge University Press, Cambridge- New York, 1989).
  • Yano, K, Ishihara, S., Tangent and Cotangent Bundles , (M. Dekker, New York, 1973).
  • Current address : Hülya KADIO ¼GLU :Department of Mathematics Education, Yildiz Technical University Istanbul TURKEY E-mail address : hkadio@yildiz.edu.tr
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Hülya Kadıoğlu Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 65 Sayı: 2

Kaynak Göster

APA Kadıoğlu, H. (2016). On the prolongations of homogeneous vector bundles. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 47-54. https://doi.org/10.1501/Commua1_0000000758
AMA Kadıoğlu H. On the prolongations of homogeneous vector bundles. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2016;65(2):47-54. doi:10.1501/Commua1_0000000758
Chicago Kadıoğlu, Hülya. “On the Prolongations of Homogeneous Vector Bundles”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, sy. 2 (Ağustos 2016): 47-54. https://doi.org/10.1501/Commua1_0000000758.
EndNote Kadıoğlu H (01 Ağustos 2016) On the prolongations of homogeneous vector bundles. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 47–54.
IEEE H. Kadıoğlu, “On the prolongations of homogeneous vector bundles”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 65, sy. 2, ss. 47–54, 2016, doi: 10.1501/Commua1_0000000758.
ISNAD Kadıoğlu, Hülya. “On the Prolongations of Homogeneous Vector Bundles”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (Ağustos 2016), 47-54. https://doi.org/10.1501/Commua1_0000000758.
JAMA Kadıoğlu H. On the prolongations of homogeneous vector bundles. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:47–54.
MLA Kadıoğlu, Hülya. “On the Prolongations of Homogeneous Vector Bundles”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 65, sy. 2, 2016, ss. 47-54, doi:10.1501/Commua1_0000000758.
Vancouver Kadıoğlu H. On the prolongations of homogeneous vector bundles. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):47-54.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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