Abstract
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.
References
- 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.
A Note On Surfaces Of Revolution Which Have Lightlike Axes Of Revolution In Minkowski Space With Density
Abstract
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.
References
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | February 28, 2020 |
| Published in Issue | Year 2020 Volume: 13 Issue: ÖZEL SAYI I |