Geodesic
On local isometric immersions into complex and quaternionic projective spaces
Archivum mathematicum, Tome 47 (2011) no. 4, pp. 251-256

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
We will prove that if an open subset of $\mathbb{C}{}P^{n}$ is isometrically immersed into $\mathbb{C}{}P^{m}$, with $m(4/3)n-2/3$, then the image is totally geodesic. We will also prove that if an open subset of $\mathbb{H}{}P^{n}$ isometrically immersed into $\mathbb{H}{}P^{m}$, with $m(4/3)n-5/6$, then the image is totally geodesic.
We will prove that if an open subset of $\mathbb{C}{}P^{n}$ is isometrically immersed into $\mathbb{C}{}P^{m}$, with $m(4/3)n-2/3$, then the image is totally geodesic. We will also prove that if an open subset of $\mathbb{H}{}P^{n}$ isometrically immersed into $\mathbb{H}{}P^{m}$, with $m(4/3)n-5/6$, then the image is totally geodesic.
Classification : 53C40
Keywords: submanifolds; homogeneous spaces; symmetric spaces 
Rivertz, Hans Jakob. On local isometric immersions into complex and quaternionic projective spaces. Archivum mathematicum, Tome 47 (2011) no. 4, pp. 251-256. http://geodesic.mathdoc.fr/item/ARM_2011_47_4_a1/
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     title = {On local isometric immersions into complex and quaternionic projective spaces},
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     zbl = {1249.53079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2011_47_4_a1/}
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