SURFACES IN $\small{\mathbb{E}^3}$ WITH L1-POINTWISE 1-TYPE GAUSS MAP

Title & Authors
SURFACES IN $\small{\mathbb{E}^3}$ WITH L1-POINTWISE 1-TYPE GAUSS MAP
Kim, Young Ho; Turgay, Nurettin Cenk;

Abstract
In this paper, we study surfaces in $\small{\mathb{E}^3}$ whose Gauss map G satisfies the equation ${\Box}G Keywords Gauss map;$\small{{\Box}}$-pointwise 1-type;Cheng-Yau operator; Language English Cited by 1. CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP,;; 대한수학회보, 2013. vol.50. 4, pp.1345-1356 2. RULED SURFACES AND GAUSS MAP,; 대한수학회보, 2015. vol.52. 5, pp.1661-1668 1. Cheng–Yau Operator and Gauss Map of Surfaces of Revolution, Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39, 4, 1319 2. Classifications of Canal Surfaces with L1-Pointwise 1-Type Gauss Map, Milan Journal of Mathematics, 2015, 83, 1, 145 3. RULED SURFACES AND GAUSS MAP, Bulletin of the Korean Mathematical Society, 2015, 52, 5, 1661 References 1. L. J. Alias and N. Gurbuz, An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures, Geom. Dedicata 121 (2006), 113-127. 2. C. Baikoussis, Ruled submanifolds with finite type Gauss map, J. Geom. 49 (1994), no. 1-2, 42-45. 3. C. Baikoussis and D. E. Blair, On the Gauss map of ruled surfaces, Glasgow Math. J. 34 (1992), no. 3, 355-359. 4. C. Baikoussis, B.-Y. Chen, and L. Verstraelen, Ruled surfaces and tubes with finite type Gauss map, Tokyo J. Math. 16 (1993), no. 2, 341-349. 5. C. Baikoussis and L. Verstralen, The Chen-type of the spiral surfaces, Results Math. 28 (1995), no. 3-4, 214-223. 6. D. D. Bleecker and J. L. Weiner, Extrinsic bounds on${\lambda}_1$of${\Delta}$on a compact manifold, Comment. Math. Helv. 51 (1976), no. 4, 601-609. 7. B.-Y. Chen, Geometry of Submanifolds, Pure and Applied Mathematics, No. 22. Marcel Dekker, Inc., New York, 1973. 8. B.-Y. Chen, On the total curvature of immersed manifolds. VI. submanifolds of finite type and their applications, Bull. Inst. Math. Acad. Sinica 11 (1983), no. 3, 309-328. 9. B.-Y. Chen, Total Mean Curvature and Submanifold of Finite Type, World Scientific, 1984. 10. B.-Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337. 11. B.-Y. Chen, M. Choi, and Y. H. Kim, Surfaces of revolution with pointwise 1-type Gauss map, J. Korean Math. Soc. 42 (2005), no. 3, 447-455. 12. B.-Y. Chen, J. M. Morvan, and T. Nore, Energy, tension and finite type maps, Kodai Math. J. 9 (1986), no. 3, 406-418. 13. B.-Y. Chen and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc. 35 (1987), no. 2, 161-186. 14. S. Y. Cheng and S. T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), no. 3, 195-204. 15. M. P. do Carmo, Riemannian Geometry, Translated from the second Portuguese edition by Francis Flaherty. Mathematics: Theory & Applications. Birkhauser Boston, Inc., Boston, MA, 1992. 16. U. Dursun, Hypersurfaces with pointwise 1-type Gauss map, Taiwanese J. Math. 11 (2007), no. 5, 1407-1416. 17. U. Dursun and N. C. Turgay, General rotational surfaces in Euclidean space${\mathbb{E}}^4$with pointwise 1-type Gauss map, Math. Commun. (accepted). 18. S. M. B. Kashani, On some$L_1$-finite type (hyper)surfaces in${\mathbb{R}}^{n+1}\$, Bull. Korean Math. Soc. 46 (2009), no. 1, 35-43.

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