Surfaces in E3 invariant under a one parameter group of isometries of E3

Fuente: Redalyc

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Ioannis M. Roussos
Format:	Artículo científico
Sprache:	en
Veröffentlicht:	Academia Brasileira de Ciências 2000
Schlagworte:	Multidisciplinaria (Ciencias Naturales y Exactas) mean group isometry Gaussian Invariant
Online-Zugang:	Acceder al recurso
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

_version_	1876432687515828224
author	Ioannis M. Roussos
author_facet	Ioannis M. Roussos
contents	Surfaces in E3 invariant under a one parameter group of isometries of E3 Ioannis M. Roussos Multidisciplinaria (Ciencias Naturales y Exactas) mean group isometry Gaussian Invariant We develop a convenient surface theory in E3 in order to apply it to the class of the surfacesinvariant under a one-parameter group of isometries of E3. In this way we derive intrinsiccharacterizations along with several results of subclasses of this class of surfaces that satisfycertain preassigned properties. In the process all results are also effortlessly derived. Among thesesubclasses are those with surfaces; of constant mean curvature, of constant Gaussian curvature,isothermic, with constant difference or ratio of the principal curvatures. 2000 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32772203 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.72
format	Artículo científico
id	redalyc_32772203
institution	Redalyc
language	en
publishDate	2000
publisher	Academia Brasileira de Ciências
spellingShingle	Surfaces in E3 invariant under a one parameter group of isometries of E3 Ioannis M. Roussos Multidisciplinaria (Ciencias Naturales y Exactas) mean group isometry Gaussian Invariant Surfaces in E3 invariant under a one parameter group of isometries of E3 Ioannis M. Roussos Multidisciplinaria (Ciencias Naturales y Exactas) mean group isometry Gaussian Invariant We develop a convenient surface theory in E3 in order to apply it to the class of the surfacesinvariant under a one-parameter group of isometries of E3. In this way we derive intrinsiccharacterizations along with several results of subclasses of this class of surfaces that satisfycertain preassigned properties. In the process all results are also effortlessly derived. Among thesesubclasses are those with surfaces; of constant mean curvature, of constant Gaussian curvature,isothermic, with constant difference or ratio of the principal curvatures. 2000 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32772203 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.72
title	Surfaces in E3 invariant under a one parameter group of isometries of E3
topic	Multidisciplinaria (Ciencias Naturales y Exactas) mean group isometry Gaussian Invariant
url	https://www.redalyc.org/articulo.oa?id=32772203

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"de"
VUFIND_SESSION	"92da97ccda1367b1908dbbcc62e49377"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791233984.1714 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "92da97ccda1367b1908dbbcc62e49377" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1763}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=de; VUFIND_SESSION=92da97ccda1367b1908dbbcc62e49377"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.28"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"52981"
REDIRECT_URL	"/Record/redalyc_32772203/Details"
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/redalyc_32772203/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791233984.167
REQUEST_TIME	1791233984

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"de"
VUFIND_SESSION	"92da97ccda1367b1908dbbcc62e49377"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791233984.1714 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "92da97ccda1367b1908dbbcc62e49377" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1763}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=de; VUFIND_SESSION=92da97ccda1367b1908dbbcc62e49377"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.28"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"52981"
REDIRECT_URL	"/Record/redalyc_32772203/Details"
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/redalyc_32772203/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791233984.167
REQUEST_TIME	1791233984

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Ähnliche Einträge

Environment & details:

Environment & details: