Additional First-Order Equation for Infinitesimal Bendings of Smooth Surfaces in the Isothermal Coordinates

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Additional First-Order Equation for Infinitesimal Bendings of Smooth Surfaces in the Isothermal Coordinates. / Alexandrov, V. A.

In: Siberian Mathematical Journal, Vol. 66, No. 3, 02.06.2025, p. 618-628.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ee632788f19a4999bc1b61bd9411256c,

title = "Additional First-Order Equation for Infinitesimal Bendings of Smooth Surfaces in the Isothermal Coordinates",

abstract = "The article contributes to the theory of infinitesimal bendings of smoothsurfaces in Euclidean 3-space.We derive a first-order linear differential equation, which previouslydid not appear in the literature and which is satisfied by any Darbouxrotation field of a smooth surface.We show that, for some surfaces, this additional equation is functionallyindependent of the three standard equations that the Darboux rotationfield satisfies (and by which it is determined).As a consequence of this additional equation, we prove the maximumprinciple for the components of the Darboux rotation field for a classof disk-homeomorphic surfaces containing not only surfaces of positive Gaussian curvature.",

keywords = "514.7, Darboux rotation field, Euclidean 3-space, elliptic partial differential equation, infinitesimal bending of a surface, isothermal coordinates, maximum principle, surface in Euclidean space",

author = "Alexandrov, {V. A.}",

note = "The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).",

year = "2025",

month = jun,

day = "2",

doi = "10.1134/S0037446625030024",

language = "English",

volume = "66",

pages = "618--628",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Additional First-Order Equation for Infinitesimal Bendings of Smooth Surfaces in the Isothermal Coordinates

AU - Alexandrov, V. A.

N1 - The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).

PY - 2025/6/2

Y1 - 2025/6/2

N2 - The article contributes to the theory of infinitesimal bendings of smoothsurfaces in Euclidean 3-space.We derive a first-order linear differential equation, which previouslydid not appear in the literature and which is satisfied by any Darbouxrotation field of a smooth surface.We show that, for some surfaces, this additional equation is functionallyindependent of the three standard equations that the Darboux rotationfield satisfies (and by which it is determined).As a consequence of this additional equation, we prove the maximumprinciple for the components of the Darboux rotation field for a classof disk-homeomorphic surfaces containing not only surfaces of positive Gaussian curvature.

AB - The article contributes to the theory of infinitesimal bendings of smoothsurfaces in Euclidean 3-space.We derive a first-order linear differential equation, which previouslydid not appear in the literature and which is satisfied by any Darbouxrotation field of a smooth surface.We show that, for some surfaces, this additional equation is functionallyindependent of the three standard equations that the Darboux rotationfield satisfies (and by which it is determined).As a consequence of this additional equation, we prove the maximumprinciple for the components of the Darboux rotation field for a classof disk-homeomorphic surfaces containing not only surfaces of positive Gaussian curvature.

KW - 514.7

KW - Darboux rotation field

KW - Euclidean 3-space

KW - elliptic partial differential equation

KW - infinitesimal bending of a surface

KW - isothermal coordinates

KW - maximum principle

KW - surface in Euclidean space

UR - https://www.mendeley.com/catalogue/559078de-a074-34b0-872b-39adea941bde/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105007138298&origin=inward&txGid=0a0111ce6759dcadff9da09498d78405

U2 - 10.1134/S0037446625030024

DO - 10.1134/S0037446625030024

M3 - Article

VL - 66

SP - 618

EP - 628

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 67703794