2022
DOI: 10.3390/sym14091914
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Timelike Circular Surfaces and Singularities in Minkowski 3-Space

Abstract: The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of tim… Show more

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Cited by 37 publications
(21 citation statements)
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“…In addition, for a special case of the (1,1)-tensor T, on Bianchi classes, some bounds of the the first non-zero eigenvalue are derived under the normalized Ricci flow. To develop this area more in the future, one can consider the techniques of the Singularity theory and Submanifold theory presented in [21][22][23][24][25][26][27][28], and it may find some new and interesting results.…”
Section: Discussionmentioning
confidence: 99%
“…In addition, for a special case of the (1,1)-tensor T, on Bianchi classes, some bounds of the the first non-zero eigenvalue are derived under the normalized Ricci flow. To develop this area more in the future, one can consider the techniques of the Singularity theory and Submanifold theory presented in [21][22][23][24][25][26][27][28], and it may find some new and interesting results.…”
Section: Discussionmentioning
confidence: 99%
“…While in reprint [36], the authors adopted this approach on a closed (compact without boundary) pointed space with a non-negative Bakry-Émery Ricci tensor.Recently, many interesting papers have been written related to symmetry, molecular cluster geometry analysis, submanifold theory, singularity theory, eigen problems, etc. [37][38][39]. In our following works, we are going to study inequalities of the Hardy type for different queries and further improve the results in this paper, combined with the technics and results in [37][38][39].…”
Section: Introductionmentioning
confidence: 94%
“…Therefore, we believe that the present article will help in achieving new and interesting results in the geometry of statistical solitons [35] on statistical submersions [36]. In fact, some singularity theories on submanifolds can be studied [14][15][16][17]. Institutional Review Board Statement: Not applicable.…”
Section: Conclusion and Remarkmentioning
confidence: 99%
“…Riemannian submersions have been intensively investigated not only in mathematics, but also in theoretical physics due to its usefulness in Kaluza Klein theory, super gravity, Yang-Mills theory, relativity, and super-string theories (see [9][10][11][12][13]). Singularity theory and submanifold theory are also crucially related to this subject and will be helpful for future research (for more details see [14][15][16][17]). The majority of Riemannian submersion investigations may be found in books [18,19].…”
Section: Introductionmentioning
confidence: 99%