# Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles

## Abstract

We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.

- Authors:

- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22364159

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; BENDING; CALCULATION METHODS; MATHEMATICAL SOLUTIONS; SMOOTH MANIFOLDS; SURFACES

### Citation Formats

```
Sabitov, I Kh.
```*Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles*. United States: N. p., 2014.
Web. doi:10.1070/SM2014V205N12ABEH004440.

```
Sabitov, I Kh.
```*Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles*. United States. doi:10.1070/SM2014V205N12ABEH004440.

```
Sabitov, I Kh. Wed .
"Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles". United States.
doi:10.1070/SM2014V205N12ABEH004440.
```

```
@article{osti_22364159,
```

title = {Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles},

author = {Sabitov, I Kh},

abstractNote = {We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.},

doi = {10.1070/SM2014V205N12ABEH004440},

journal = {Sbornik. Mathematics},

number = 12,

volume = 205,

place = {United States},

year = {Wed Dec 31 00:00:00 EST 2014},

month = {Wed Dec 31 00:00:00 EST 2014}

}

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