Journals / Gazi Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2002 / Cilt: 15 - Sayı: 2

Transversal simetrik afin immersiyonlar üzerine

Pages
467–473
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

After, some relationship between the affine invariants of the original immersion and the affine invariant of the transversallly symmetric immmersion are found.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a new affine immersion is obtained by using the vector field which is associated with an affine immersion.
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Key Findings & Data:This immersion is called transversally symmetric immersion since it is the symmetry of the original immersion according to the transversal vector field.
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Conclusion & Impact:After, some relationship between the affine invariants of the original immersion and the affine invariant of the transversallly symmetric immmersion are found.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, a new affine immersion is obtained by using the vector field which is associated with an affine immersion. This immersion is called transversally symmetric immersion since it is the symmetry of the original immersion according to the transversal vector field. After, some relationship between the affine invariants of the original immersion and the affine invariant of the transversallly symmetric immmersion are found.

Özet

Bu çalışmada ;bir afin immersiyon ile eşleştirilen vektör alanını kullanarak,yeni bir afin immersiyon elde edildi. Bu immersiyona; transversal vektör alanına göre orijinal immersiyonun simetriği olması nedeniyle, transversal simetrik afin immersiyon denildi. Sonra ,Orijinal afin immersiyon ile transversal simetriğinin afin invaryantları arasında, bazı bağıntılar bulundu.

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Cite This Article

YAKUT, A. T., KARLIĞA, B. (2022). Transversal simetrik afin immersiyonlar üzerine. Gazi Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 15 - Sayı: 2, 467–473. https://ajindex.com/articles/522324

References (1)

  1. [I]Tzitzeica, G., Sur une nouvelle classe de surfaces, Rend. Circ. Mat. Palermo, 25(1908), 180-187; 28 (1909), 210-216. [2]Blaschke, W., Vorlesungen über Differentialgeometrie II,Affîne Differentialgeometrie, Springer, Berlin, 1923. [3]Cartan, E., Sur la Connexion Affine des Surfaces, C. R. Acad. Sci. Paris, 178(1924), 292-295. [4] Slebodzinski, W., Sur quelques problemes de la theorie des surfaces de l'espace affîne, Prace Mat. Fiz., 46(1939), 291-345. [5]Schirokow, P.A. and Schirokow, A.P., Affine Differentialgeometrie, Teubner, Leibzig, 1962. [6]Guggenheimer, H., Differential Geometry, McGraw-Hill, New York 1963. [7]Spivak, M., A Comprehensive Introduction to Differential Geometry,I-V, Publish or Perish, Berkeley, California, 1970-1975. [8]Nomizu, K. and Sasaki, T., On a theorem of Chern and Terng on affine surfaces, Manuscripta Math., 73(1991), 39-44. [9]Verheyen, P. and Verstraelen, L., Locally symmetric affine hypersurfaces, Proc. Amer. Math.Soc, 93(1985), 101-105. [10] Nomizu, K. and Pinkall, U., On the geometry of affine immersions, Math. Z., 195(1987), 165-178. I11] Dillen, F.,Locally symmetric complex affine hypersurfaces, J. Geom., 33(1988), 27-38. [12]Nomizu, K. and Sasaki, T., Affine Differential Geometry: geometry of affine immersions. Cambridge University Press, 1994.