Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold

Rok, strany: 2020, 497 - 503

If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types $\{3⁶\},$ $\{4⁴\}$ and $\{6³\}$ on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types $\{3³, 4²\},$ $\{3², 4¹, 3¹, 4¹\}, $ $\{3¹, 6¹, 3¹, 6¹\},$ $ \{3⁴, 6¹\},$ $\{4¹, 8²\}, $ $\{3¹, 12²\}, $ $\{4¹,6¹, 12¹\}$ and $\{3¹, 4¹, 6¹, 4¹\}$ on the torus. This gives a partial solution to the well known Conjecture that every $4$-connected graph on the torus has a Hamiltonian cycle.

ISO 690:

Maity, D., Upadhyay, A. 2020. Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold. In Mathematica Slovaca, vol. 70, no.2, pp. 497-503. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0367

APA:

Maity, D., Upadhyay, A. (2020). Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold. Mathematica Slovaca, 70(2), 497-503. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0367

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava