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LSpice
LSpice
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I am considering Laplacian eigenvalues of a geodesic sphere in the octonion projective plane and I would like to know the metric on a geodesic sphere.

Does the metric on a geodesic sphere in the octonion projective plane is a canonical variation associated with the Riemannian submersion $\pi : \mathbb{S}^{15} \rightarrow \mathbb{O}P^1 $ from the octonion Hopf fibration?

Loosely speaking, canonical variation on a metric associated with the Riemannian submersion with totally geodesic fibers is a variation on the given metric only in the fiber. More precise definition can be found in p. 191, Section 5, Berard-Bergery and Bourguignon [Illinois Journ of Math, 1982]- Laplacians and Riemannian submersions with totally geodesic fibres [Illinois Journ of Math, 1982] (MSN).

I am considering Laplacian eigenvalues of a geodesic sphere in the octonion projective plane and I would like to know the metric on a geodesic sphere.

Does the metric on a geodesic sphere in the octonion projective plane is a canonical variation associated with the Riemannian submersion $\pi : \mathbb{S}^{15} \rightarrow \mathbb{O}P^1 $ from the octonion Hopf fibration?

Loosely speaking, canonical variation on a metric associated with the Riemannian submersion with totally geodesic fibers is a variation on the given metric only in the fiber. More precise definition can be found in p. 191, Section 5, Berard-Bergery and Bourguignon [Illinois Journ of Math, 1982].

I am considering Laplacian eigenvalues of a geodesic sphere in the octonion projective plane and I would like to know the metric on a geodesic sphere.

Does the metric on a geodesic sphere in the octonion projective plane is a canonical variation associated with the Riemannian submersion $\pi : \mathbb{S}^{15} \rightarrow \mathbb{O}P^1 $ from the octonion Hopf fibration?

Loosely speaking, canonical variation on a metric associated with the Riemannian submersion with totally geodesic fibers is a variation on the given metric only in the fiber. More precise definition can be found in p. 191, Section 5, Berard-Bergery and Bourguignon - Laplacians and Riemannian submersions with totally geodesic fibres [Illinois Journ of Math, 1982] (MSN).

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Donghwi Seo
Donghwi Seo
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Geodesic sphere in the octonion projective plane

I am considering Laplacian eigenvalues of a geodesic sphere in the octonion projective plane and I would like to know the metric on a geodesic sphere.

Does the metric on a geodesic sphere in the octonion projective plane is a canonical variation associated with the Riemannian submersion $\pi : \mathbb{S}^{15} \rightarrow \mathbb{O}P^1 $ from the octonion Hopf fibration?

Loosely speaking, canonical variation on a metric associated with the Riemannian submersion with totally geodesic fibers is a variation on the given metric only in the fiber. More precise definition can be found in p. 191, Section 5, Berard-Bergery and Bourguignon [Illinois Journ of Math, 1982].