Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 3 min ago
PreprintarXiv licencearXiv

Harmonic maps from spheres with lowest possible index and their properties

  • Surkov Egor
Open at sourcePDFDOICite

Abstract

In this note, we prove that for n > 2 a harmonic map π•Šn β†’ β„‚β„™m, of index n+1 is pseudo horizontally weakly conformal, that n must be odd. In particular, for even n every non-constant harmonic map π•Šn β†’ β„‚β„™m has index at least n+2. We also present a harmonic map from π•Š4 to Grβ„‚(2,4) of index 5 that is not pseudo horizontally weakly conformal, so the statement does not extend to Grassmannians.

Related

  1. New GAPN functions with the lowest possible algebraic degree
    Noureddine El-Asri, Valentin Suder
    Finite Fields and Their ApplicationsPeer-reviewedCC BY 4.0Full textGeneral mathematicsHAL
  2. Partial regularity of heat flow of fractional harmonic maps to spheres
    Hengrong Du, Tao Huang, Armin Schikorra +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Sharp Harmonic-Mean Bounds for Neumann Eigenvalues on Riemannian Surfaces and Counterexamples to Geodesic Ball Optimality on Higher-Dimensional Spheres
    Hongtao Hu, Meiqi Liu, Qiaoran Wu +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. The Morse Index, Nullity and Jacobi Fields of Constant-Curvature Minimal 2-Spheres in Complex Projective Spaces
    Hongbin Cui, Shuping Huang
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Stability analysis of the Lane--Emden equation of index n=5 describing polytropic gas spheres
    S. C. Mancas, Ronald Adams
    arXivPreprintarXiv licenceFull textSolar & stellar physicsMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{egor2026harmonic,
  title = {{Harmonic maps from spheres with lowest possible index and their properties}},
  author = {Surkov Egor},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35589},
  eprint = {2609.35589},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35589},
}
RIS
TY  - UNPB
TI  - Harmonic maps from spheres with lowest possible index and their properties
AU  - Surkov Egor
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35589
UR  - https://arxiv.org/abs/2609.35589
AB  - In this note, we prove that for n > 2 a harmonic map π•Š^n β†’ β„‚β„™^m, of index n+1 is pseudo horizontally weakly conformal, that n must be odd. In particular, for even n every non-constant harmonic map π•Š^n β†’ β„‚β„™^m has index at least n+2. We also present a harmonic map from π•Š^4 to Gr_β„‚(2,4) of index 5 that is not pseudo horizontally weakly conformal, so the statement does not extend to Grassmannians.
ER  -