The symbolic Corinthian helmet in Greek, Etruscan, and Roman art

Etruscan culture was influenced by ancient Greek culture, beginning around 750 BCE, during the last phase of the Villanovan period, when the Greeks, who were at this time in their Archaic Orientalizing period, started founding colonies in southern Italy.  It continued during the Classical period from the 5th to the 4th centuries BCE, even though the political balance of power in the region began to shift to the rising Roman Republic after 500 BCE.

The bearded warrior depicted in an Etruscan finial sculpture at the Metropolitan Museum of Art, which originally decorated the top of a tall candelabrum, wears a Greek Corinthian-style helmet tipped back on his head.  This practice gave rise to a series of variant forms in Italy, where the slits were almost closed, since the helmet was no longer pulled over the face but worn cap-like. In the Republican Roman army,  the Corinthian helmet evolved into a jockey-cap style helmet called the Italo-Corinthian, Etrusco-Corinthian or Apulo-Corinthian helmet, with the characteristic nose guard and eye slits becoming mere decorations on its face. The Italo-Corinthian types remained in use until the 1st century CE. 

Although the style gradually gave way to the more open Thracian, Chalcidian, and the much simpler pilos type helmet, which was less expensive to manufacture and did not obstruct the wearer's critical senses of vision and hearing, the Corinthian helmet was depicted on more sculpture than any other helmet as, apparently, the Greeks romantically associated it with glory and the past. The Romans also revered it, depicting it on their copies of Greek original art as well as sculpture of their own. 

Bronze finial of two warriors from a candelabrum ca. 480–470 BCE, Etruscan, courtesy of the Metropolitan Museum of Art.  This finial, which originally decorated the top of a tall candelabrum, is an excellent example of Early Classical sculpture. A bearded warrior wearing a full panoply of armor assists his younger, beardless comrade, who has sustained a wound to his left leg or foot and is supported by the spear he once held in his right hand and by his friend's shoulder. - Metropolitan Museum of Art.

Composite image I created of Greek helmets on display at the Staatliche Antikensammlungen Museum in Munich, Germany.  From left to right: Phrygian, Illyrian, Pileus, Corinthian, and Chalcidian helmets originally photographed by Wikimedia Commons contributor MisterPlus65.