This research proves the intrinsic nature of normalized second fundamental forms in hypersurfaces, indicating a new understanding of geometry.
We prove that the normalized second fundamental form A of immersed C² hypersurface in a space form (Nⁿ⁺¹, g) is intrinsic provided σ₂ₖ₊₁(A)≠ 0 for some k≥ 1. We also establish the intrinsicality of the normalized second fundamental form A of Mⁿ=∂Ω for domain Ω⊂ Nⁿ⁺¹, \ n≥ 3.
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Guan et al. (2025) studied this question.
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