Yoğunluklu Minkowski Uzayında Lightlike Dönme Eksenli Dönel Yüzeyler Üzerine Bir Not

Bu çalışmada, yoğunluk Minkowski uzayında lightlike dönme eksenli dönel yüzeyleri çalıştık. Üzerinde çalıştığımız dönel yüzeylerin üreteç eğrisinin, yüzeyin Gauss eğriliği yardımıyla elde ettiğimiz ikinci dereceden lineer olmayan diferansiyel denklemin bir çözümü olduğunu gördük. Bu diferansiyel denklemin çözerek dönel yüzeyin denklemini elde ettik. Son olarakta el ettiğimiz dönel yüzeylerin grafiklerini çizdik.

Anahtar Kelimeler:

Minkowski uzayı, yoğunluklu manifold, ağırlıklı eğrilik, dönel yüzeyler

A Note On Surfaces Of Revolution Which Have Lightlike Axes Of Revolution In Minkowski Space With Density

In this paper, we study surfaces of revolution which have lightlike axes of revolution in Minkowski space with density. The generating curve of these surfaces satisfies a non-linear second order differential equation which describes the prescribed weighted Gaussian curvature. By solving differential equation we get surfaces of revolution. Also, we draw a graph of the surface of revolution. Also, we draw a graph of the surface of revolution.

Keywords:

Minkowski space, manifold with density, weighted curvature, surfaces of revolution,

PDF

___

Beneki, C. C., Kaimakamis, G., and Papantoniou, B. J. 2002. “Helicoidal surfaces in three-dimensional Minkowski space” Journal of Mathematical Analysis and Applications,275(2), 586-614.
Corwin, I., Hoffman, N., Hurder, S., Sesum V. and Xu, Y. “Differential geometry of manifolds with density”, Rose-Hulman Undergrad.Math. J,. 7 1-15.
Delaunay, C. H. 1841. “Sur la surface de r´evolution dont la courbure moyenne est constante” Journal de math´ematiques pures et appliqu´ees 309-314
Hano, J. I. and Nomizu, K. 1984. “Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space”, Tohoku Mathematical Journal, Second Series, 36(3), 427-437.
Hsiang, W. and Yu, W. 1981. “A generalization of a theorem of Delaunay”, J. Differential Geometry, 16, 161-177.
Kenmotsu, K. 1980. “Surfaces of revolution with prescribed mean curvature”. Tohoku Mathematical Journal, Second Series 32(1), 147-153.
Morgan, F. (2016). “Geometric measure theory: a beginner’s guide”, Academic press, .Morgan, F. 2005. “Manifolds with density”, Notices of the AMS, 853-858.
Morgan, F. 2006 “Myers’ theorem with density”, Kodai Mathematical, Journal 29(3), 455- 461.
Morgan, F. 2009. “Manifolds with Density and Perelman’s Proof of the Poincar´e Conjecture”, American Mathematical Monthly, 116(2), 134-142
Rayon, P. and Gromov, M. 2003. “Isoperimetry of waists and concentration of maps”, Geometric and functional analysis, 13(1), 178-215.