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Abstract This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that$$\alpha $$ -positive/$$\alpha $$ -nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all$$\alpha \in [1,5]$$ .
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Frobenius-like structure in Gaudin model
We introduce a Frobenius-like structure for the [Formula: see text] Gaudin model. Namely, we introduce potential functions of the first and second kind. We describe the Shapovalov form in terms of derivatives of the potential of the first kind and the action of Gaudin Hamiltonians in terms of derivatives of the potential of the second kind.
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- Award ID(s):
- 1954266
- PAR ID:
- 10411629
- Date Published:
- Journal Name:
- International Journal of Mathematics
- Volume:
- 33
- Issue:
- 07
- ISSN:
- 0129-167X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0129167X22500525
