The rima glottidis is the opening between the true vocal cords and the arytenoid cartilages.

It is normally subdivided into two parts, that between the arytenoid cartilages is called the intercartilaginous part (or the intercartilaginous glottis, respiratory glottis, or interarytenoid space), and that between the vocal folds

Vocal folds

The vocal folds, also known commonly as vocal cords, are composed of twin infoldings of mucous membrane stretched horizontally across the larynx...

 the intermembranous part or glottis vocalis.

It is closed by the lateral cricoarytenoid and arytenoid muscle

Arytenoid muscle

The arytenoid is a single muscle, filling up the posterior concave surfaces of the arytenoid cartilages.It arises from the posterior surface and lateral border of one arytenoid cartilage, and is inserted into the corresponding parts of the opposite cartilage.It consists of oblique and transverse...

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It is opened by the Posterior cricoarytenoid muscle

Posterior cricoarytenoid muscle

The posterior cricoarytenoid muscles are extremely small, paired muscles that extend from the posterior cricoid cartilage to the arytenoid cartilages in the larynx. By rotating the arytenoid cartilages laterally, these muscles abduct the vocal cords and thereby open the rima glottidis. Their action...

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All of these muscles receive their innervation from the Recurrent laryngeal nerve

Recurrent laryngeal nerve

The recurrent laryngeal nerve is a branch of the vagus nerve that supplies motor function and sensation to the larynx . It travels within the endoneurium...

 which is a branch of the Vagus nerve

Vagus nerve

The vagus nerve , also called pneumogastric nerve or cranial nerve X, is the tenth of twelve paired cranial nerves...

 (CNX). This nerve can be vulnerable in thyroid

Thyroid

The thyroid gland or simply, the thyroid , in vertebrate anatomy, is one of the largest endocrine glands. The thyroid gland is found in the neck, below the thyroid cartilage...

 surgery, if damaged control to the rima glottidis may be affected resulting in a hoarse voice, aphonia

Aphonia

Aphonia is the inability to speak. It is considered more severe than dysphonia. A primary cause of aphonia is bilateral disruption of the recurrent laryngeal nerve, which supplies nearly all the muscles in the larynx...

or difficulty breathing.