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1996•Tokyo Journal of MathematicsOpen access

Extrinsic Characterizations of Circles in a Complex Projective Space Imbedded in a Euclidean Space

Bang‐Yen Chen, Sadahiro Maeda

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Abstract

$0$ . Introduction. It is well-known that a curve on a sphere $S^{2}$ in $R^{3}$ is a geodesic (that is, a great circle) or a (small) circle if and only if it is a circle as a curve in $R^{3}$ . This can be considered as an extrinsic characterization of circles on $S^{2}$ in $R^{3}$ . On the other hand, Adachi, Udagawa and the second author ([1]) investigate circles in a complex projective space $CP^{n}(c)$ of constant holomorphic sectional curvature

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$0$ . Introduction. It is well-known that a curve on a sphere $S^{2}$ in $R^{3}$ is a geodesic (that is, a great circle) or a (small) circle if and only if it is a circle as a curve in $R^{3}$ . This can be considered as an extrinsic characterization of circles on $S^{2}$ in $R^{3}$ . On the other hand, Adachi, Udagawa and the second author ([1]) investigate circles in a complex projective space $CP^{n}(c)$ of constant holomorphic sectional curvature

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Available abstract

$0$ . Introduction. It is well-known that a curve on a sphere $S^{2}$ in $R^{3}$ is a geodesic (that is, a great circle) or a (small) circle if and only if it is a circle as a curve in $R^{3}$ . This can be considered as an extrinsic characterization of circles on $S^{2}$ in $R^{3}$ . On the other hand, Adachi, Udagawa and the second author ([1]) investigate circles in a complex projective space $CP^{n}(c)$ of constant holomorphic sectional curvature

Key concepts: Mathematics, Complex projective space, Sectional curvature, Pure mathematics, Geodesic, Real projective space, Holomorphic function, Quaternionic projective space

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