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The Morse Index, Nullity and Jacobi Fields of Constant-Curvature Minimal 2-Spheres in Complex Projective Spaces

  • Hongbin Cui
  • Shuping Huang
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Abstract

We determine the Morse index and normal nullity of all constant-curvature minimal two-spheres in complex projective spaces, identify the normal Jacobi kernel as an SU(2)-module, and prove that every normal Jacobi field is integrable. The formulas include all totally geodesic extensions. In a fixed ambient space, the normal nullity is constant along each Veronese sequence.

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Cite

BibTeXRIS
BibTeX
@misc{cui2026morse,
  title = {{The Morse Index, Nullity and Jacobi Fields of Constant-Curvature Minimal 2-Spheres in Complex Projective Spaces}},
  author = {Hongbin Cui and Shuping Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.00922},
  eprint = {2609.00922},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00922},
}
RIS
TY  - UNPB
TI  - The Morse Index, Nullity and Jacobi Fields of Constant-Curvature Minimal 2-Spheres in Complex Projective Spaces
AU  - Hongbin Cui
AU  - Shuping Huang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00922
UR  - https://arxiv.org/abs/2609.00922
AB  - We determine the Morse index and normal nullity of all constant-curvature minimal two-spheres in complex projective spaces, identify the normal Jacobi kernel as an SU(2)-module, and prove that every normal Jacobi field is integrable. The formulas include all totally geodesic extensions. In a fixed ambient space, the normal nullity is constant along each Veronese sequence.
ER  -