Finally, we give neccessary andsufficient condition for a normal section to be a W-curve on pseudo-Riemannian submanifolds.
📌 3 Key Takeaways
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Objective & Hypothesis:In the present paper we study pseudo-Riemannian submanifolds whichhave 3-planar geodesic normal sections.We consider W-curves (helices)on pseudo-Riemannian submanifolds.
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Key Findings & Data:In the present paper we study pseudo-Riemannian submanifolds whichhave 3-planar geodesic normal sections.We consider W-curves (helices)on pseudo-Riemannian submanifolds.
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Conclusion & Impact:Finally, we give neccessary andsufficient condition for a normal section to be a W-curve on pseudo-Riemannian submanifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Pseudo-Riemann Altmanifoldlar · Geodezik normal kesitler · Pseudo-Riemannian submanifold
Abstract
In the present paper we study pseudo-Riemannian submanifolds whichhave 3-planar geodesic normal sections.We consider W-curves (helices)on pseudo-Riemannian submanifolds. Finally, we give neccessary andsufficient condition for a normal section to be a W-curve on pseudo-Riemannian submanifolds.
Özet
Bu makalede, 3-düzlemsel normal kesitlere sahip Pseudo-Riemann Altmanifoldları çalıştık.Pseudo-Riemann Altmanifoldları üzerinde W-eğrilerini(helis) ele aldık. Son olarak, Pseudo-Riemann Altmanifoldları üzerindebir normal kesitin W-eğrisi olması için gerek ve yeter koşulu verdik.
ÖZTÜRK, G., ARSLAN, K., BULCA, B. (2017). Pseudo-Riemannian Submanifolds with 3-planar Geodesics. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 2 - Sayı: 1, 107–112. https://ajindex.com/articles/415176
Arslan K. and Celik Y., Submanifolds in real space form with 3-planar geodesic normal sections, Far East J.Math.Sci. 5(1) (1997), 113-120
Arslan K., Celik Y. and Deszcz R., A note on geodesic circles on Riemannian manifolds, Far East J.Math.Sci. 5(3) (1997), 453-459
Arslan K., Lumiste U., Murathan C. and Ozgur C., 2-Semiparallel surfaces in space forms I,two particular cases, Proc. Estonian Acad.Sci. Phys. Math. 49 (2000),, 139-148
Arslan K. and West A.,Product submanifolds with P.3-PNS., Glasgow J. Math. 37 (1995), 73-81
Blomstrom C., Planar geodesic immersions in pseudo-Euclidean space, Math. Ann. 274 (1986), 585-598
Chen B. Y.,Geometry of submanifolds, Marcel-Dekker, 1973
Chen B. Y., Geometry of submanifolds and its applications, Science University of Tokyo 1981
Ferus, D., Immersions with parallel second fundamental form, Math. Z 140 (1974), 87-92
Ferus D. and Schirrmacher S., Submanifolds in Euclidean space with simple geodesics, Math. Ann. 260 (1982), 57-62
Hong S.L., Isometric immersions of manifolds with plane geodesics in Euclidean space, J. Dif. Geo. 8 (1973), 259-278
Iawa, T., On some curves in Riemannian geometry, Soochow J. Math. 7 (1980), 37-44
Iawa, T., On curves and submanifolds in an inde nite-Riemannian manifold, Tukuba J. Math. 9 (1985), 353-371
Kim Y.H., Minimal surface of pseudo-Euclidean spaces with geodesic normal sections, Dif. Geo. and its App. 5 (1995), 321-329
Kim Y.H., Surfaces in a pseudo-Euclidean space with planar normal sections, J. Geom. 35 (1989), 120-131
Li S.J., Isotropic submanifolds with pointwise 3-planar normal sections, Boll. U. M. I. 7 (1987), 373-385
Li S.J., Spherical submanifolds with pointwise 3 or 4-planar normal sections, Yokohoma Math. J. 35 (1987), 21-31
Little J. A., Manifolds with planar geodesics, J. Diff. Geom. 11 (1976) 265-285
Lumiste U., Submanifolds with Vander Waerden-Bortolotti plane connection and parallelism of the third fundamental form, Izv.Vuzov.Mat. 30(1987), 18-27
Murathan C., Pointwise k-planar normal sections with Immersions in warped products of Riemannian manifolds, PhD Thesis, Uludag University, (1995), Bursa-Turkey
Nakagawa H., On a certain minimal immersion of a Riemannian manifold into a sphere, Kodai Math. 3 (1980), 321-340
Nakanishi Y., On helices and pseudo-Riemannian submanifolds, Tsukuba J. Math. 12 (1988), 459-476