Gradient Ricci Solitons on PTR-Submanifolds of Complex Space Forms
Abstract
We study gradient Ricci solitons on partially totally real (PTR) submanifolds of complex space forms. In nonzero ambient holomorphic sectional curvature, the Gauss--soliton equation reconstructs the square P2 of the tangential Kähler operator from the Hessian endomorphism and an extrinsic Ricci operator. Consequently, the PTR tangency spectrum is encoded by intrinsic soliton data together with the second fundamental form. For compact minimal PTR solitons with positive ambient curvature we obtain λ≤ c(n−1)/4, with a strict version under a relative-nullity condition. We also prove compact triviality criteria, an exact trace-free anisotropy identity, a parallel-data rigidity result, and a nonexistence theorem for compact real hypersurfaces. A flat multi-level Gaussian model and a nonflat Segre CR-product provide explicit consistency checks and identify the limiting cases of the reconstruction formulas.
Related
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- Steady gradient Ricci Yang-Mills solitons on 2-orbifolds
- Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature
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BibTeX
@misc{lee2026gradient,
title = {{Gradient Ricci Solitons on PTR-Submanifolds of Complex Space Forms}},
author = {Jae Won Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00077},
eprint = {2610.00077},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00077},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gradient Ricci Solitons on PTR-Submanifolds of Complex Space Forms
AU - Jae Won Lee
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00077
UR - https://arxiv.org/abs/2610.00077
AB - We study gradient Ricci solitons on partially totally real (PTR) submanifolds of complex space forms. In nonzero ambient holomorphic sectional curvature, the Gauss--soliton equation reconstructs the square P^2 of the tangential Kähler operator from the Hessian endomorphism and an extrinsic Ricci operator. Consequently, the PTR tangency spectrum is encoded by intrinsic soliton data together with the second fundamental form. For compact minimal PTR solitons with positive ambient curvature we obtain λ≤ c(n−1)/4, with a strict version under a relative-nullity condition. We also prove compact triviality criteria, an exact trace-free anisotropy identity, a parallel-data rigidity result, and a nonexistence theorem for compact real hypersurfaces. A flat multi-level Gaussian model and a nonflat Segre CR-product provide explicit consistency checks and identify the limiting cases of the reconstruction formulas.
ER -