### Abstract

If x : M^{n}⟶ E^{m} is an isometric immersion of a smooth manifold into a Euclidean space then the map x = xx^{t} (t denotes transpose) is called the quadric representation of M . x is said to be of finite type (fc-type) if it can be decomposed into a sum of finitely many (k) eigenfunctions of Laplacian from different eigenspaces. We study map x in general, especially as related to the condition of being of finite type. Certain classification results are obtained for manifolds with 1-and 2-type quadric representation.

Original language | English (US) |
---|---|

Pages (from-to) | 201-210 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 114 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1992 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Proceedings of the American Mathematical Society*, vol. 114, no. 1, pp. 201-210. https://doi.org/10.1090/S0002-9939-1992-1086324-1

**Quadric representation of a submanifold.** / Dimitrić, Ivko.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quadric representation of a submanifold

AU - Dimitrić, Ivko

PY - 1992/1

Y1 - 1992/1

N2 - If x : Mn⟶ Em is an isometric immersion of a smooth manifold into a Euclidean space then the map x = xxt (t denotes transpose) is called the quadric representation of M . x is said to be of finite type (fc-type) if it can be decomposed into a sum of finitely many (k) eigenfunctions of Laplacian from different eigenspaces. We study map x in general, especially as related to the condition of being of finite type. Certain classification results are obtained for manifolds with 1-and 2-type quadric representation.

AB - If x : Mn⟶ Em is an isometric immersion of a smooth manifold into a Euclidean space then the map x = xxt (t denotes transpose) is called the quadric representation of M . x is said to be of finite type (fc-type) if it can be decomposed into a sum of finitely many (k) eigenfunctions of Laplacian from different eigenspaces. We study map x in general, especially as related to the condition of being of finite type. Certain classification results are obtained for manifolds with 1-and 2-type quadric representation.

UR - http://www.scopus.com/inward/record.url?scp=84968484473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968484473&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1992-1086324-1

DO - 10.1090/S0002-9939-1992-1086324-1

M3 - Article

AN - SCOPUS:84968484473

VL - 114

SP - 201

EP - 210

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -