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.
Downloads
Download data is not yet available.
References
[1] Aminov Yu. The Geometry of Submanifolds. Gordon and Breach Science Publishers, Amsterdam, 2001.
[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.
[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://scitecresearch.com/journals/index.php/jprm/article/view/1970
Issue
Section
Articles
Copyright (c) 2021 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.