On Curvatures of the Torus Hypersurface in 4-Space
Keywords:
four space, torus hypersurface, curvatures
Abstract
We study curvatures of torus hypersurface in the four dimensional Euclidean space. We also give some relations on of torus hypersurface.
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References
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[9] Krasko E. Omelchenko A. Enumeration of r-regular maps on the torus. Part I: rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus. Discrete Math. 342 (2019), no. 2, 584–599.
[10] Krasko E., Omelchenko A. Enumeration of r-regular maps on the torus. Part II: Unsensed maps. Discrete Math. 342(2), (2019) 600–614.
[11] Lerman L. M., Trifonov K.N. The Topology of Symplectic Partially Hyperbolic Automorphisms of the 4-Torus. (Russian) Mat. Zametki 108(3), (2020) 474–476.
[12] Mase M. Families of K3 surfaces and curves of (2,3)-torus type. Kodai Math. J. 42 (2019), no. 3, 409–430.
[13] Nakamura S. The orthonormal Strichartz inequality on torus. Trans. Amer. Math. Soc. 373(2), (2020) 1455–1476.
[14] Poletti, Mauricio Geometric growth for Anosov maps on the 3 torus. Bull. Braz. Math. Soc. (N.S.) 49 (2018), no. 4, 699–713.
[15] Sakajo T. Vortex crystals on the surface of a torus. Philos. Trans. Roy. Soc. A 377(2158), (2019) 1–17.
[2] Borovitskiĭ V.A. K-closedness for weighted Hardy spaces on the torus T2. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 456 (2017), Issledovaniya po Lineĭnym Operatoram i Teorii Funktsiĭ. 45, 25–36; translation in J. Math. Sci. (N.Y.) 234(3), (2018) 282–289.
[3] Dasgupta J., Khan B., Uma V. Cohomology of torus manifold bundles. Math. Slovaca 69(3), (2019) 685–698.
[4] Duston C.L. Torus solutions to the Weierstrass-Enneper representation of surfaces. J. Math. Phys. 60(8), (2019) 1–5.
[5] Harvey J., Searle C. Almost non-negatively curved 4-manifolds with torus symmetry. Proc. Amer. Math. Soc. 148(11) (2020), 4933–4950.
[6] Hasegawa M., Ida D. Instability of stationary closed strings winding around flat torus in five-dimensional Schwarzschild spacetimes. Phys. Rev. D 98(4) (2018) 1–7.
[7] Hirose S., Kin E. On hyperbolic surface bundles over the circle as branched double covers of the 3-sphere. Proc. Amer. Math. Soc. 148(4), (2020) 1805–1814.
[8] Kamiyama Y. The orbit space of a hypersurface of a torus by an involutıon. J. Geom. Top. 21(4), (2018) 365–372.
[9] Krasko E. Omelchenko A. Enumeration of r-regular maps on the torus. Part I: rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus. Discrete Math. 342 (2019), no. 2, 584–599.
[10] Krasko E., Omelchenko A. Enumeration of r-regular maps on the torus. Part II: Unsensed maps. Discrete Math. 342(2), (2019) 600–614.
[11] Lerman L. M., Trifonov K.N. The Topology of Symplectic Partially Hyperbolic Automorphisms of the 4-Torus. (Russian) Mat. Zametki 108(3), (2020) 474–476.
[12] Mase M. Families of K3 surfaces and curves of (2,3)-torus type. Kodai Math. J. 42 (2019), no. 3, 409–430.
[13] Nakamura S. The orthonormal Strichartz inequality on torus. Trans. Amer. Math. Soc. 373(2), (2020) 1455–1476.
[14] Poletti, Mauricio Geometric growth for Anosov maps on the 3 torus. Bull. Braz. Math. Soc. (N.S.) 49 (2018), no. 4, 699–713.
[15] Sakajo T. Vortex crystals on the surface of a torus. Philos. Trans. Roy. Soc. A 377(2158), (2019) 1–17.
Published
2021-05-17
How to Cite
Güler, E. (2021). On Curvatures of the Torus Hypersurface in 4-Space. Journal of Progressive Research in Mathematics, 18(2), 5-10. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/1970
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