Research Article

Some remarks on the moment curves in R4 and R3

Volume: 3 Number: 1 June 24, 2025
Istanbul Journal of Mathematics Cover
Istanbul Journal of Mathematics
PDF Download

Some remarks on the moment curves in R4 and R3

Abstract

The moment curves and their normalizations are key tools in obtaining the famous Kac formula from the theory of random polynomials. We study here the normalized moment curves Γ𝑛 ∈ 𝑆𝑛 in the low dimensions 𝑛 where 𝑆𝑛 is the Euclidean 𝑛 dimensional unit sphere; more precisely we consider 𝑛 = 3 and 𝑛 = 2. First, we compute the image of the normalized moment curve Ξ“3 under the well-known Hopf fibre map and show that this remarkable map reduces the length of Ξ“3. Second, we analyze the curve Ξ“2 using the theory of spherical Legendre curves. An image of Ξ“2 is included.

Keywords

References

  1. Crasmareanu, M., 2016, Chin. Ann. Math., Ser. B, 37, no. 3, 419-426. google scholar
  2. Crasmareanu, M., 2021, Mat. Vesn., 73, no. 4, 256-267. google scholar
  3. Crasmareanu, M., 2024, Turkish J. Math., 48, no. 4, 749-756. google scholar
  4. Crasmareanu, M., 2024, Chapter in: Bang-Yen Chen et al (Eds.), "Geometry of Submanifolds and Applications", Infosys Science Foundation Series, Springer, 197-207. google scholar
  5. Edelman, A., Kostlan, E., 1995, Bull. Am. Math. Soc., 32, no. 1, 1-37. google scholar
  6. Takahashi, M., 2016, In: Nabarro, Ana Claudia et al (Eds.), "Real and complex singularities", AMS Contemporary Mathematics 675, 337-355. google scholar

Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Publication Date

June 24, 2025

Submission Date

January 28, 2025

Acceptance Date

May 16, 2025

Published in Issue

Year 2025 Volume: 3 Number: 1

DOI

https://doi.org/10.26650/ijmath.2025.00024

IZ

https://izlik.org/JA27PZ94GA

Cite

RIS / Bibtex
APA
Crasmareanu, M. (2025). Some remarks on the moment curves in R4 and R3. Istanbul Journal of Mathematics, 3(1), 34-38. https://doi.org/10.26650/ijmath.2025.00024
AMA
1.Crasmareanu M. Some remarks on the moment curves in R4 and R3. Istanbul Journal of Mathematics. 2025;3(1):34-38. doi:10.26650/ijmath.2025.00024
Chicago
Crasmareanu, Mircea. 2025. β€œSome Remarks on the Moment Curves in R4 and R3”. Istanbul Journal of Mathematics 3 (1): 34-38. https://doi.org/10.26650/ijmath.2025.00024.
EndNote
Crasmareanu M (June 1, 2025) Some remarks on the moment curves in R4 and R3. Istanbul Journal of Mathematics 3 1 34–38.
IEEE
[1]M. Crasmareanu, β€œSome remarks on the moment curves in R4 and R3”, Istanbul Journal of Mathematics, vol. 3, no. 1, pp. 34–38, June 2025, doi: 10.26650/ijmath.2025.00024.
ISNAD
Crasmareanu, Mircea. β€œSome Remarks on the Moment Curves in R4 and R3”. Istanbul Journal of Mathematics 3/1 (June 1, 2025): 34-38. https://doi.org/10.26650/ijmath.2025.00024.
JAMA
1.Crasmareanu M. Some remarks on the moment curves in R4 and R3. Istanbul Journal of Mathematics. 2025;3:34–38.
MLA
Crasmareanu, Mircea. β€œSome Remarks on the Moment Curves in R4 and R3”. Istanbul Journal of Mathematics, vol. 3, no. 1, June 2025, pp. 34-38, doi:10.26650/ijmath.2025.00024.
Vancouver
1.Mircea Crasmareanu. Some remarks on the moment curves in R4 and R3. Istanbul Journal of Mathematics. 2025 Jun. 1;3(1):34-8. doi:10.26650/ijmath.2025.00024